How did Edmond Halley determine that the comets of 1531, 1607, and 1682 were the same comet?

In 1705, English astronomer Edmond Halley published A Synopsis of the Astronomy of Comets, in which he calculated the orbits of 24 comets observed between 1337 and 1698.1

By analyzing these data, Halley observed that the comets recorded in 1531, 1607, and 1682 exhibited remarkably similar orbital characteristics and appeared at regular intervals of approximately 76 years. Using Isaac Newton's methods and the law of universal gravitation, Halley concluded that these were not three separate objects, but rather the same comet returning to the inner solar system at periodic intervals.2134

Based on this finding, he successfully predicted that the comet would return in 1758. Although Halley died before this date, the comet was recovered on schedule, confirming his theory and establishing it as the first recognized periodic comet, now known as Halley’s Comet.231