I'm just reading Augustine's City of God, and he argues that the darkening of the Sun mentioned in the gospel accounts could not be explained by a lunar eclipse, because the crucifixion occurred at passover which is always a full moon, and eclipses always occur during the "last quarter" of the moon.
Firstly, what does "last quarter" mean for the Romans? Eclipses only occur during new moons - is that consider the "last quarter" in Roman reckoning, or is he mistaken?
Secondly, is this just an empirical observation based on historical reports, or did the Romans actually have a physical model for how eclipses work? That is, did Augustine say that eclipses happen during the last quarter just because historians had noted that eclipses always happen at this phase, or did Augustine say this because the Romans actually knew that the Moon had to be in the correct position for an eclipse to occur?
The Greeks reportedly knew how to predict them as far back as 585 BC. Herodotus gives an account in The Histories:
...just as the battle was growing warm, day was on a sudden changed into night. This event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing for it the very year in which it actually took place.
We also know that Claudius Ptolemy, a Roman citizen, had worked out how to predict both Solar and Lunar eclipses with a very clever and sophisticated model during the Second Century, detailed in his Almagest. It's not unreasonable to suggest that Augustine may have had knowledge of the works of Ptolemy, given that it had been so long since its publication.
I had difficulty identifying anything about the Romans' beliefs surrounding solar eclipses, but there's a semi-famous account in Plutarch's Parallel Lives about a lunar eclipse on the night before the Battle of Pydna, almost 600 years before the birth of Augustine:
When it was night, and, supper being over, all were turning to sleep and rest, on a sudden the moon, which was then at full and high in the heavens, grew dark, and by degrees losing her light, passed through various colors, and at length was totally eclipsed. The Romans, according to their custom, clattering brass pans and lifting up firebrands and torches into the air, invoked the return of her light; the Macedonians behaved far otherwise: terror and amazement seized their whole army, and a rumor crept by degrees into their camp that this eclipse portended even that of their king. Aemilius was no novice in these things, nor was ignorant of the nature of the seeming irregularities of eclipses, that in a certain revolution of time, the moon in her course enters the shadow of the earth and is there obscured, till, passing the region of darkness, she is again enlightened by the Sun.
So although at least some amongst the Romans certainly knew the cause of such events in that time, they nevertheless still took part in religious rituals intended to bring back the Moon's light. Even Aemilius subsequently took part in sacrifices (which Plutarch describes in detail), despite knowing that it was a natural occurrence.