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. 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 formula_16 and formula_17, the latitudes of Alexandria and the Hellespontine region, respectively. He also would have known formula_18, the declination of the Moon during the eclipse, and formula_19, which is related to the difference in totality of the eclipse between the two regions. Crd here refers to the chord function. Since the Moon is very distant, it follows that formula_21. Using this approximation gives  Hence,  With formula_27 and formula_28, we only need formula_19 to get formula_30. Because the eclipse was total at H, and 4/5 total at A, it follows that formula_19 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 formula_32. Toomer determined how Hipparchus determined the chord for small angles (see Chord (geometry)). His values for the latitudes of the Hellespont (41 degrees) and Alexandria (31 degrees) are known from Strabo's work on Geography. To determine the declination, it is necessary to know which eclipse Hipparchus used. Because he knew the value which Hipparchus eventually gave for the distance to the Moon (71 Earth radii) and the rough region of the eclipse, Toomer was able to determine that Hipparchus used the eclipse of March 14, 190 BC.