Why did Edmond Halley predict that the comet of 1682 would return in 1758?

Edmond Halley predicted the return of the comet of 1682 by applying the principles of celestial mechanics developed by his friend Isaac Newton to historical data.12

In 1705, Halley published a catalog of the orbits of 24 comets. Upon analyzing the data, he observed that the comets recorded in 1531, 1607, and 1682 shared remarkably similar orbital characteristics and appeared at regular intervals of approximately 76 years.32

Although the observations at the time were only sufficient to calculate parabolic orbits, Halley hypothesized that these sightings were actually the same object traveling in a closed, eccentric elliptical orbit around the Sun. Based on this periodic pattern, he accurately predicted that the comet would return in 1758. While Halley did not live to witness the event, the comet was recovered in late 1758, confirming his theory and establishing it as the first recognized periodic comet.132