Parallax is the difference in position between two objects along two lines of sight, the distance is measured by the inclined angle between the two. In Astronomy, this is applied to measure the stellar parallax on stars, and their distance from the earth with accurate astrometry. The Ancient Greeks, with their belief in the earth at the center of the universe, not only did they not have the technology, but they also were not looking for this as an explanation. The process of stellar parallax was extremely difficult to achieve, and distances are measured by red-shift calculations on a galactic scale.
