In 1717 Halley compared contemporaneous measurements of the latitudes of four stars with earlier measurements by ancient Greek astronomers and by Brahe, and from the differences concluded that these four stars showed proper motion. An analysis with modern methods shows that the data used by Halley do not contain significant evidence for proper motion. What Halley found are the measurement errors of Ptolemaios and Brahe. Halley further argued that the occultation of Aldebaran by the Moon on 11 March 509 in Athens confirmed the change in latitude of Aldebaran. In fact, however, the relevant observation was almost certainly made in Alexandria where Aldebaran was not occulted. By carefully considering measurement errors Jacques Cassini showed that Halleys results from comparison with earlier astronomers were spurious, a conclusion partially confirmed by various later authors. Cassinis careful study of the measurements of the latitude of Arcturus provides the first significant evidence for proper motion.