In ST 2-2.96.1, as part of his discussions of observantiae or observances that are associated with the vice of superstition, Thomas Aquinas discusses the ars notoria. Interestingly, this is an article in which the Dominican Fathers translation is not very good at all.* The translation has the generic "magical arts", "magic art", and (once) "notary art". In all of these, Thomas Aquinas speaks specifically of the ars notoria. The notory (not notary) art is a very specific tradition of magical practice, and one that was particularly tempting to monks and friars and the like, because it was for the purpose of learning arts and sciences.
The ars notoria is notoria because it uses notae, which are magical diagrams. In fact, 'notory' is the English word for 'involving the use of magical symbols and diagrams', and derives etymologically from this particular art. These notae were used in invocations of (usually) angels and (sometimes) demons and beings of the air. As such it is a part of a broader tradition of Solomonic arts, called so because they are connected with legends of King Solomon. The notory art in particular was said to have been delivered to Solomon by the angel Pamphilius on golden tablets, containing various diagrams and prayers and invocations associated with using them. We don't know for sure how exactly the diagrams played a role; they are often similar to images used in ordinary non-magical mnemonic arts, but also to common ordinary devotional symbols. It's possible that they were guides to prayer, like the latter, or that they served as a kind of memory palace, like the former. Since the notory art is heavily associated in what literature we have with visions, they may have been deliberately used to facilitate visions.
St. Thomas is quite vehement in his judgment of the ars notoria: ars notoria et illicita est, et inefficax. In all of his discussion of superstitious observances, St. Thomas is guided by a text by St. Augustine which talks of "compacts by tokens with demons". Direct agreements with demons are associated with nigromantia (black magic) or necromantia (death magic) -- medieval Latin does not make a sharp distinction between the two. However, the ars notoria involves no direct agreements with demons; rather, as St. Thomas sees it, it creates an implicit compact with demons by using signs in ways that attempt to direct spirits of any kind. Notorists usually intended to invoke angels rather than demons, of course, but I don't think Aquinas would consider this particularly relevant; demons, after all, are angels, and use such signs to delude the unwary. Aquinas is not against use of signs of various kinds in prayer; but acceptable signs are either divinely instituted (whether directly by God or indirectly by God's giving the Church authority in matters of prayer) or are signs used in the ordinary way to convey meaning.
What fundamentally bothers St. Thomas when it comes to the notory art is that its means are inappropriate to its end. The notae are not causes of knowledge; they are usually pretty basic geometrical symbols, sometimes written with various words, letters, and numbers. Inspection of them will not itself give you understanding of the liberal arts or the sciences. Rather, they are only signs that are used when invoking spirits to give you knowledge. And the invocations themselves are attempts to bypass the way of coming to know that is appropriate to human nature (acquisitio scientiae per modum homini connaturalem), namely, the way of discovery and study. God sometimes gives knowledge without discovery or study, but this is not something that can be had by any art, since it is purely a matter of grace, and it is given not for one's own personal interest in learning but for the good of the Church. The ars notoria, of course, is an alleged ars, intended to cause knowledge; but it's actually spirits, whom the invoker cannot actually control, who are supposed to provide the results. In fact, only God can directly enlighten the intellect; Aquinas is very clear that angels, demons, and any other spirits there might be cannot generally do so. When the notory art gets its results, therefore, they are necessarily sham; even if it were actually invoking only angels, angels cannot directly give us knowledge, and the same is true of demons. The demons instead influence our imagination in deceptive and misleading ways. Thus the actual practices are nugatory (nugatoria) and poisonous (noxia) when it comes to real learning.
While Aquinas discusses the art on general principles, it's perhaps worth noting that actual experience with the notory art seems to conform with his discussion, as far as we know it. Notorists tended to treat the art as effective, contrary to Aquinas, of course, but when you look at the specifics of what they claimed to have learned, it's not particularly impressive, and often just involves remembering things more easily. And we have recorded experiences in late medieval literature of people trying the notory art and finding that it gave them terrible nightmares and repulsive visions.
This little article in the Summa, easily overlooked by us, actually played a significant role in the history of magic, because Aquinas's discussion was a major influence on the Church's late medieval condemnations of all varieties of notory art, which were often quite harsh. The late medieval Church was often also worried about the occasionally similarities between notorial and necromantic figures, but this is a secondary issue. St. Thomas gives the first and essential principle explaining why the notory art is illicit in itself: the way one acquires knowledge must be appropriate to the intellect itself. If the signs had a direct causal contribution to your knowledge (as geometrical diagrams do), there would be no problem, because they would just be part of our intellectual discovery; if the prayers were just prayers to God for aid, they would be ordinary religious piety and would not themselves be any sort of substitute for ordinary study; but as mere signs that are associated with invoking spirits, they are superstitious rites inappropriate to learning -- a completely futile attempt to get spirits to do your learning for you, an unnatural endeavor that is both bad for your intellectual life and an abuse of your relationship with the spiritual world.
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* Looking into this further, it appears that the translation at New Advent (cited as the Second and Revised edition of 1920) is different from some others. This version of the translation, from 1922, is somewhat better, although still in some ways flawed.