Thomas Aquinas, Compendium of Theology

Since the agent intellect and the possible intellect are united to us as form, we must acknowledge that they pertain to the same essence of the soul. Whatever is formally united to another thing, is united to it either in the manner of a substantial form or in the manner of an accidental form. If the possible intellect and the agent intellect were united to man after the fashion of a substantial form, we would have to hold that they share in the one essence of that form which is the soul, since one thing cannot have more than one substantial form. On the other hand, if they are united to man after the fashion of an accidental form, neither of them, evidently, can be an accident of the body. Besides, the fact that their operations are performed without a bodily organ, as we proved above, shows that each of them is an accident of the soul. But there is only one soul in one man. Therefore the agent intellect and the possible intellect must inhere in the one essence of the soul.

Furthermore, every action that is proper to a species proceeds from principles that emanate from the form which confers the species. But the action of understanding is an operation proper to the human species. Therefore the agent intellect and the possible intellect, which are principles of this action, as has been shown, emanate from the human soul, whence man has his species. However, they do not issue from the soul in such a way as to extend to the body, because, as we have said, the operation in question takes place independently of a bodily organ. Since, therefore, action pertains to the same subject as does potency, the possible intellect and the agent intellect inhere in the one essence of the soul.