When were solar eclipses first predicted accurately?
The Babylonians knew how to predict lunar eclipses with some accuracy, but solar eclipses are far more difficult because the 'footprint' on the Earth is only a few tens of miles across and requires arc minute positional accuracy and forecasting for any specific locale. Apparently Thales, c. 610 B.C. E, is credited with predicting a solar eclipse from knowledge of a previous eclipse and using the Saros cycle. He predicted the year, but not the month and the day. It wasn't until Ptolemy's time that solar eclipse forecasting became more accurate.