How did Ptolemy explain the apparently irregular movements of the planets?

Ptolemy explained the apparently irregular movements of the planets by postulating that these paths were actually a combination of several regular circular motions, viewed from a stationary Earth.12

To account for these observations within the Ptolemaic system, he utilized two primary mechanisms:

• Epicyclic Model: Each planet revolved uniformly along a smaller circular path called an epicycle. The center of this epicycle simultaneously revolved around Earth along a larger circular path known as the deferent. Because the epicycle's motion could run counter to the deferent, it effectively explained why planets appeared to slow down or reverse direction, a phenomenon known as retrograde motion.1
• Eccentricity and the Equant: Ptolemy incorporated eccentricity by displacing the center of a planet's path from Earth. He further refined this by introducing the equant, a point from which the epicycle's center appeared to sweep out equal angles in equal times, allowing for accurate predictions of varying planetary speeds.1