I just received an email from Harold Remus who pointed me to an interesting article on a mechanism designed to compute solar eclipses and to arrange the calendar in connection with the cycles of the Olympiad (ancient Olympics). The New York Times article explains:
The Antikythera Mechanism, sometimes called the first analog computer, was recovered more than a century ago in the wreckage of a ship that sank off the tiny island of Antikythera, north of Crete. Earlier research showed that the device was probably built between 140 and 100 B.C.
The full article is available here: Discovering How Greeks Computed in 100 B.C.