How did Edmond Halley discover that Sirius and Arcturus change position relative to other stars?

In 1718, the English astronomer Edmond Halley discovered that the stars Sirius and Arcturus had shifted their positions relative to their neighbors. He made this discovery by comparing their then-current positions with the data recorded in the Almagest, a star catalog compiled by the ancient Greek astronomer Ptolemy.

This finding marked the first detection of what is now known as proper motion, which refers to the apparent movement of a star across the celestial sphere. While Halley also incorrectly announced proper motions for the stars Aldebaran and Betelgeuse, his work on Sirius and Arcturus successfully demonstrated that stars are not truly fixed in the sky, as had been previously assumed.12