What evidence did Ptolemy use to argue that Earth is spherical?

In his foundational work, the Almagest, Ptolemy established the cosmological framework for his geocentric system by presenting empirical arguments for the Earth being a stationary sphere at the center of the universe.12

While earlier Greek thinkers like Aristotle had previously argued for a spherical Earth based on the circular shadow cast on the Moon during a lunar eclipse and the changing visibility of stars as one travels north or south, Ptolemy synthesized these observations to support his model. He maintained that the heavens, including the stars and planets, revolve around this central, spherical Earth.3451

Ptolemy’s approach was rooted in the belief that celestial motions could be explained through precise mathematical and geometric terms, setting the standard for astronomy for over a millennium. By treating the Earth as a sphere, he was able to apply spherical trigonometry to calculate astronomical phenomena and planetary positions with unprecedented accuracy for his time.126