I. In I Sent., 8, 1, 1, c
II. In I Sent., 8, 4, 2, ad 2
III. In I Sent., 8, 5, 2, c
IV. In III Sent., 11, 1, 2, ad 2
V. De Veritate, 1, 1, c
VI. De Veritate, 1,1, ad 1
VII. De Veritate, 1, 1, ad sc 3
VIII. De Veritate, 10, 8, ad 13
IX. Summa Theologiae, I, 3, 4, ad 2
X. De Potentia, 7, 2, ad 1
XI. Quaestiones Quodlibetales, 9, 4, 1, c
XII. In Metaphysicorum, 4, 2, No. 6
XIII. In De Hebdomadibus, 2
Commentary on Text VIII: De Veritate, 10, 8, ad 13
Ad decimumtertium dicendum, quod intellectiva potentia est forma ipsius animae quantum ad actum essendi, eo quod habet esse in anima, sicut proprietas in subiecto; sed quantum ad actum intelligendi nihil prohibet esse e converso.
"The intellective power is a form of the soul with reference to its ‘act of being,’ for it exists in the soul as a property in a subject. But there is nothing to prevent the opposite of this, from being true with reference to the act of understanding."
In this text Aquinas makes use of the principle of metaphysical priority. The application of metaphysical priority to the notion of ‘act’ results in the following gradation of acts:
Pure Act (God)
Actus Essendi (the metaphysical principle that goes with ‘essence’)
Substantial Form (which exists in both spiritual and material beings)
Accidental Form (like the intelligence of men and angels)
Activity of Accidental Forms (like reasoning in man)
Products of Certain Activities of Accidental Forms (like a conclusion reached after a process of reasoning)
In the text, Aquinas mentions four acts: 1) the actus essendi, 2) the soul--a substantial form, 3) the faculty of the intellect--an accidental form, and 4) the act of understanding--an activity of an accidental form.
Now, from the perspective of the actus essendi, it makes sense to say that the intellectual faculty of man inheres in the soul because the metaphysical principle of actus essendi refers to a self-subsisting individual that is actually existing here and now.
De Veritate, 10, 8, ad 13, expresses this as follows: "The intellective power is a form of the soul with reference to its ‘act of being,’ for it exists in the soul as a property in a subject." (Intellectiva potentia est forma ipsius animae quantum ad actum essendi, eo quod habet esse in anima, sicut proprietas in subiecto.)
But with respect to the activity of the intellectual faculty, the soul could be made the content of our thinking. The intellectual faculty of man can direct its activity towards getting information about our soul. In this sense, the soul informs, ‘gives form,’ to our act of understanding.
Note on Translation: The expression "actus essendi" is translated into English as "act of being," into Italian as "atto di essere," into French as "acte d'être," into Spanish as "acto de ser," and into German as "Akt des Seins" ("Seinsakt.")