Then substracted two times the avarage period of revolution of Halley's Comet, and came to 2194 BC.
Then (or even before that) he checked if that date would be 1656 years after the 3850 BC date for the Creation (calculated straightforward), and voila, 2194 BC we have.
Then add a chart like Puzzler posted of the heavens during the Vernal Equinox around 21 September (end of the summer) 2914 BC (nicely close to the Pleiades) and we have a bingo, lol.
Abramelin, according to JPL, Halley's Comet performs one complete revolution around the sun every 75.32 years. Since the last known observance of it was in 1986 we can determine the dates in which it appeared in the 22nd century BC. There is only one (1) date in that timeframe. That date is 2157 BC, which interestingly enough is close to the 2160 BC date for the extreme drought that caused the collapse of the Old Kingdom in Ancient Egypt.
JPL Information on Halley's Comet
Edited to correct a typo. Thanks Abe for catching that.
Edited by cormac mac airt, 04 January 2012 - 07:12 PM.