What did Edmond Halley describe in A Synopsis of the Astronomy of Comets?

In his 1705 work A Synopsis of the Astronomy of Comets, the British scientist Edmond Halley described the parabolic orbits of 24 comets that had been observed between 1337 and 1698.12

By analyzing these data, Halley noted that the comets recorded in 1531, 1607, and 1682 exhibited remarkably similar characteristics and orbital paths. He concluded that these were not separate objects, but rather the same comet returning to the inner solar system at regular intervals of approximately 76 years. Based on this finding, he successfully predicted that the comet would return in 1758. Although Halley did not live to witness the event, the comet's reappearance confirmed his theory, establishing it as the first recognized periodic comet, now known as Halley’s Comet.1324