what value Hipparchus actually used although, when the lunar model was taken over later by Ptolemy, he computed a ratio of 5 4 : 60.

Hipparchus' parameters were based on Babylonian observations of lunar eclipses. As a result, the model worked well at full moons but, as Ptolemy demonstrated 300 years later with observations of the Moon at other points in its orbit, it did not work well away from the syzygies. With his solar and lunar theories, Hipparchus created the first coherent theory of eclipses. Durations could be determined about as accurately as they could be measured, but the time at which the eclipse would occur was predicted less well. This situation did not improve substantially until the work of Tycho Brahe at the end of the sixteenth century.

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