How did Ptolemy use his model to predict solar and lunar eclipses?

Ptolemy utilized his geocentric mathematical model of the universe, detailed in his work the Almagest, to predict solar and lunar eclipses by calculating the precise positions and motions of the Sun and Moon relative to Earth.12

While earlier astronomers like Hipparchus had established foundational methods for observing these phenomena, Ptolemy is credited with refining these into a fully predictive lunar model. In Book 6 of the Almagest, he applied his geometric theories—which accounted for the irregular apparent motions of celestial bodies through combinations of uniform circular motions like epicycles and eccentricity—to determine when the Sun and Moon would align in a way that produced an eclipse. By modeling these paths, he could forecast the timing and characteristics of eclipses, a practice that remained a standard guide for astronomers for over a millennium.3124