The catalogue that opens the Lemegeton did not begin with seventy-two entries.
Its direct ancestor is the Pseudomonarchia Daemonum, a list appended by the Dutch physician Johann Weyer to the fifth edition of his De Praestigiis Daemonum in 1577. Weyer enumerates sixty-nine spirits. The count is not a matter of interpretation: the entries are numbered, and the last of them carries the number sixty-nine.
The discrepancy is visible inside Weyer's own pages. His entry for Belial repeats the old story of the brazen vessel in which Solomon is said to have confined the spirits, and reports that shut up within it were seventie two kings, chief among them Bileth, Beliall and Asmoday. So a text that could produce only sixty-nine names was already asserting the number seventy-two. The catalogue and the claim did not agree.
The Goetia closes the gap. It carries sixty-eight of Weyer's spirits, drops one, Pruflas, also written Bufas, and adds four that Weyer does not have at all: Vassago, Seere, Dantalion and Andromalius. Sixty-nine, less one, plus four, is seventy-two.
Why seventy-two rather than seventy or eighty is nowhere stated in the manuscripts, and any answer is an inference. But it is difficult to separate the number from the Shem ha-Mephorash, the seventy-two-fold divine name derived from three verses of Exodus, which by the seventeenth century had been circulating in Christian Kabbalah for over a hundred years. Seventy-two binding angels and seventy-two bound spirits make a symmetry, and the arrangement associated with Thomas Rudd sets them against one another name for name.
The direction of the fitting is the point worth holding on to. The angel list is the older and the more fixed. The demon list is the one that was adjusted to match it.