The Babylonians knew how to predict lunar eclipses with high accuracy, but solar eclipses are far more difficult because the 'footprint' on the earth is only a few tens of miles across and requires arcminute positional accuracy and forecasting for any specific locale. Apparently Thales ca 610 BC is credited with predicting a solar eclipse using knowledge of a previous eclipse 47 years before and adding 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 precise and useful.