We clearly infer from this that God, who moves all things, must Himself be immovable. If He, being the first mover, were Himself moved, He would have to be moved either by Himself or by another. He cannot be moved by another, for then there would have to be some mover prior to Him, which is against the very idea of a first mover. If He is moved by Himself, this can be conceived in two ways: either that He is mover and moved according to the same respect, or that He is a mover according to one aspect of Him and is moved according to another aspect. The first of these alternatives is ruled out. For everything that is moved is, to that extent, in potency, and whatever moves is in act. Therefore if God is both mover and moved according to the same respect, He has to be in potency and in act according to the same respect, which is impossible. The second alternative is likewise out of the question. If one part were moving and another were moved, there would be no first mover Himself as such, but only by reason of that part of Him which moves. But what is per se is prior to that which is not per se. Hence there cannot be a first mover at all, if this perfection is attributed to a being by reason of a part of that being. Accordingly the first mover must be altogether immovable.
Among things that are moved and that also move, the following may also be considered. All motion is observed to proceed from something immobile, that is, from something that is not moved according to the particular species of motion in question, Thus we see that alterations and generations and corruptions occurring in lower bodies are reduced, as to their first mover, to a heavenly body that is not moved according to this species of motion, since it is incapable of being generated, and is incorruptible and unalterable. Therefore the first principle of all motion must be absolutely immobile.
St. Thomas Aquinas. (1265-1274). Compendium Theologiae: The Immobility of God, trans. by Cyril Vollert. St. Louis, MO: B. Herder Book Co., 1947
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