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1

I am going to second dotancohen's answer somewhat. Hipparchus developed a comprehensive astronomy that accurately predicted eclipses and other astronomical events. Ptolemy's writings emanate from the tradition that was established by Hipparchus. Nevertheless, Hipparchus was certainly not the beginning of Greek astronomy. He simply formalized and improved ...


4

Wikipedia has an informative article on the Saros cycle, which is used to predict eclipses. According to that page, and by extension apparently the pages to which it references, the Babylonians were recording the eclipses which describe the cycle in the sixth century BC. Apparently Hipparchus (second century BC), Pliny (first century AD) and Ptolemy (second ...


3

From a NASA answer: Ptolemy ( ca 150 BC)[sic] represents the epitome of Greecian astronomy, and surviving records show that he had a sophisticated scheme for predicting both lunar and solar eclipses. Ptolemy knew, for example, the details of the orbit of the Moon including its nodal points, and that the Sun must be within 20d 41' of the Node point, and ...


2

This detailed article argues for the authenticity of Herodotus' report about Thales ecplise prediction in 585 BC. This is in any case a lot earlier than the Chinese material cited by Semaphore.


18

(This is an incomplete answer since I don't know which eclipse specifically was predicted, nor how it compares to the rest of the world. But it is s too long for a comment.) Because of their cultural association of governmental legitimacy with astronomical / geophysical omens, ancient China was rather obsessed with predicting eclipses. Attempts to do so ...



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