Among Vine's offices is the discovery of witches. It is a small line, and it sits in the middle of the bloodiest period of European witch prosecution, which makes it one of the more uncomfortable sentences in the book.
The chronology is not incidental. Weyer compiled the ancestor of this catalogue in the 1570s, at the height of the persecutions, and he compiled it in order to argue against them. Reginald Scot, whose English translation of Weyer is the demonstrated source of the Goetia's text, wrote The Discoverie of Witchcraft in 1584 for the same purpose: to show that the accused were deluded, ill or defrauded, and that the confessions were worthless. James VI of Scotland is reported to have ordered Scot's book burned.
So the Goetia's catalogue descends, by a traceable line, from two consecutive attempts to stop people being executed for witchcraft. And in the course of that descent it acquired an entry advertising a spirit who will identify witches.
Nothing about that is a paradox in the period's own terms. Learned ritual magic and popular witchcraft were understood as different things by the people who practised the first, and cunning folk who claimed to detect witches were a fixture of English village life and appear constantly in the court records. The compiler was not being ironic.
But it is a clean illustration of what happened to Weyer's work. A sceptic's exhibit, printed to be disbelieved, was excerpted into a working catalogue and put to exactly the use its author had written against. Whatever else the Lemegeton is, on this point it is a monument to a book being read backwards.