This is in Wired today!:

585 B.C.: A solar eclipse in Asia Minor brings an abrupt halt to a battle, as the warring armies lay down their arms and declare a truce. Historical astronomy later sets a likely date, providing a debatable calculation point for pinning down some dates in ancient history.

This was not the first recorded solar eclipse. After failing to predict one such in 2300 B.C., two Chinese astrologers attached to the emperor's court were soon detached from their heads. Clay tablets from Babylon record an eclipse in Ugarit in 1375 B.C. Later records identify total solar eclipses that "turned day into night" in 1063 and 763 B.C.

But the 585 B.C. eclipse was the first we know that was predicted. The Greek historian Herodotus wrote that Thales of Milete predicted an eclipse in a year when the Medians and the Lydians were at war. Using the same calculating methods that predict future eclipses, astronomers have been able to calculate when eclipses occurred in the past. You can run the planetary clock in reverse as well as forward. To coin a word, you can postdict as well as predict.

The most likely candidate for Thales' eclipse took place on May 28, 585 B.C., though some authorities believe it may have been 25 years earlier in 610 B.C. Hundreds of scholars have debated this for nearly two millenniums.

Predicting a solar eclipse is not easy. You need to calculate not only when it will happen, but where it will be visible. In a lunar eclipse, when the moon passes through the Earth's huge sun shadow, the event is visible on the whole side of the Earth that's in nighttime, and totality often lasts more than an hour. But in a solar eclipse, the moon's shadow falls across the Earth in a relatively narrow path, and the maximum duration of totality at any given place is only about 7½ minutes.

So you need to know the moon's orbit in great detail -- within a small fraction of a degree of arc. The early Greeks did not have this data.

We do not know the method Thales used to make his prediction. The method may have been used only once, because we have no other records of the Greeks of this era accurately predicting further eclipses. Thales is believed to have studied the Egyptians' techniques of land measurement (geo metry in Greek) later codified by Euclid. One has to wonder whether Thales made the famous eclipse prediction himself, or if he simply borrowed it from the Egyptians.

However he made the prediction, and however precise or vague it may have been, the eclipse occurred. Aylattes, the king of Lydia, was battling Cyaxares, king of the Medes, probably near the River Halys in what is now central Turkey.

The heavens darkened. Soldiers of both kings put down their weapons. The battle was over. And so was the war.

After 15 years of back-and-forth fighting between the Medes and the Lydians, the kings of Cilicia and Babylon intervened and negotiated a treaty. The River Halys, where the Battle of the Eclipse was fought, became the border between the Lydians and the Medes.