Thomas Aquinas, Compendium of Theology

The conclusion is evident that there can be but one God. If there were many gods, they would be called by this name either equivocally or univocally. If they are called gods equivocally, further discussion is fruitless; there is nothing to prevent other peoples from applying the name "god" to what we call a stone. If they are called gods univocally, they must agree either in genus or in species. But we have just shown that God can be neither a genus nor a species comprising many individuals under Himself. Accordingly a multiplicity of gods is impossible.

Again, that whereby a common essence is individuated cannot pertain to many. Although there can be many men, it is impossible for this particular man to be more than one only. So if an essence is individuated by itself, and not by something else, it cannot pertain to many. But the divine essence is individuated by itself, since God's essence is not distinct from His existence; for we have shown that God is His essense. Hence God cannot be more than one only.

Another consideration is the following. A form can be multiplied in two ways: first, by specific differences, as in the case of a generic form; in this way color is differentiated into the various species of color; secondly, by the subjects in which it inheres, for example, whiteness. Therefore any form incapable of being multiplied by specific differences cannot be multiplied at all, if it is a form that does not exist in a subject. Thus whiteness, if it were to subsist without a subject, would not be more than one. But the divine essence is very existence, ipsum esse, which does not admit of specific differences, as we have shown. Since, therefore, the divine existence is a quasi-form subsisting by itself, seeing that God is His existence, the divine essence cannot be more than one. Accordingly a plurality of gods is impossible.