Swerdlow suggested that Hipparchus had estimated 490 Earth radii as a minimum possible distance to the Sun. This distance corresponds to a solar parallax of 7', which may have been the maximum that he thought would have gone unnoticed (the typical resolution of the human eye is 2'). The formula obtained above for the distance to the Sun can be inverted to determine the distance to the Moon: Using the same values as above for each angle, and using 490 earth radii as the minimum solar distance, it follows that the maximum mean lunar distance is Toomer expanded on this by observing that as the distance to the Sun increases without bound, the formula approaches a minimum mean lunar distance: This is close to the value later claimed by Ptolemy. Book 1 reconstruction (Toomer) In addition to explaining the minimum lunar distance that Hipparchus achieved, Toomer was able to explain the method of the first book, which employed a solar eclipse. Pappus states that this eclipse was total in the region of the Hellespont, but was observed to be 4/5 of total in Alexandria. If Hipparchus assumed that the Sun was infinitely distant (i.e. that "the earth has the ratio of a point and center to the sun"), then the difference in magnitude of the solar eclipse must be due entirely to the parallax of the Moon. By using observational data, he would be able to determine this parallax, and hence the distance of the Moon. Hipparchus would have known and , the latitudes of Alexandria and the Hellespontine region, respectively. He also would have known , the declination of the Moon during the eclipse, and , which is related to the difference in totality of the eclipse between the two regions. Crd here refers to the chord function, which maps an angle in degrees to the corresponding length of a chord of a circle of unit diameter. Since the Moon is very distant, it follows that . Using this approximation gives Hence, With and , we only need to get . Because the eclipse was total at H, and 4/5 total at A, it follows that is 1/5 of the apparent diameter of the Sun. This quantity was well known by Hipparchus—he took it to be 1/650 of a full circle. The distance from the center of the Earth to the Moon then follows from . Toomer determined how