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Hipparchus (Astronomer): Sun
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In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, which Toomer (against the opinion of over a century of astronomers) presumes to be the eclipse of 14 March 190 BC. It was total in the region of the Hellespont (and in fact in his birth place Nicaea); at the time Toomer proposes the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita VIII.2. It was ... observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont about 40° North.
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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
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Hipparchus ... undertook to find the distances and sizes of the Sun and the Moon. He published his results in a work of two books called Peri megethoon kai 'apostèmátoon ("On Sizes and Distances") by Pappus in his commentary on the Almagest V.11; Theon of Smyrna (2nd century) mentions the work with the addition "of the Sun and Moon".
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Using this calculation, Swerdlow was able to relate the two results of Hipparchus (67 1/3 for the moon and 490 for the sun). Obtaining this relationship exactly requires following a very precise set of approximations.
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