Final answer:
The 223 gear on the Antikythera Mechanism is significant because it indicates the lunar apogee, showcasing the advanced ancient Greek understanding of astronomy and engineering.
Step-by-step explanation:
The significance of the 223 gear on the Antikythera Mechanism is that it indicates the lunar apogee, which is the point in the moon's elliptical orbit where it is furthest from the Earth. This complex gearing system was used by ancient Greek scientists to track celestial phenomena with remarkable precision. The Antikythera Mechanism is an early example of an analog computer, demonstrating the advanced knowledge of astronomy and engineering possessed by astronomers and engineers in the ancient world.