rejected by Noel Swerdlow in 1969. G. J. Toomer expanded on his efforts in 1974. Hultsch Friedrich Hultsch determined in a 1900 paper that the Pappus source had been miscopied, and that the actual distance to the Sun, as calculated by Hipparchus, had been 2490 Earth radii (not 490). As in English, there is only a single character difference between these two results in Greek. His analysis was based on a text by Theon of Smyrna which states that Hipparchus found the Sun to be 1880 times the size of the Earth, and the Earth 27 times the size of the Moon. Assuming that this refers to volumes, it follows that and Assuming that the Sun and Moon have the same apparent size in the sky, and that the Moon is 67 Earth radii distant, it follows that This result was generally accepted for the next seventy years, until Noel Swerdlow reinvestigated the case. Book 2 reconstruction (Swerdlow) Swerdlow determined that Hipparchus relates the distances to the Sun and Moon using a construction found in Ptolemy. It would not be surprising if this calculation had been originally developed by Hipparchus himself, as he was a primary source for the Almagest. Using this calculation, Swerdlow was able to relate the two results of Hipparchus (67 for the Moon and 490 for the Sun). Obtaining this relationship exactly requires following a very precise set of approximations. Using simple trigonometric identities gives and By parallel lines and taking t = 1, we get By similarity of triangles, Combining these equations gives The values which Hipparchus took for these variables can be found in Ptolemy's Almagest IV, 9. He says Hipparchus found that the Moon measured its own circle close to 650 times, and that the angular diameter of Earth's shadow is 2.5 times that of the Moon. Pappus tells us that Hipparchus took the mean distance to the Moon to be 67. This gives: According to Swerdlow, Hipparchus now evaluated this expression with the following roundings (the values are in sexagesimal): and Then, because it follows that Swerdlow used this result to argue that 490 was the correct reading of the Pappus text, thus invalidating Hultsch' interpretation. While this result is highly dependent on the particular approximations and roundings used, it has generally been accepted. It leaves open, however, the question of where the lunar distance 67 came from. Following Pappus and Ptolemy,