My rough translation of Thomas Aquinas, Summa Theologiae 1.3.7. The Latin is here, the Dominican Father translation is here.
*******************************************
It seems that God is not wholly simple. For whatever is from God, imitates Him; thus all beings are from first being, and all goods are from first good. But in things that are from God, there is nothing wholly simple. Therefore God is not wholly simple.
Further, all that is best is attributed to God. But with us, the composite are better than the simple, as bodies mixed from elements than elements that are their parts. Therefore it must be said that God is not wholly simple.
But to the contrary is what Augustine says (Trin. VI), that God is truly and supremely simple.
I reply that it must be said that God's being wholly simple can be manifested in many ways.
First, by what is said above. For in God there is no composition -- neither of quantitative parts, because He is not a body; nor composition of form and matter; nor in Him are nature and supposit other; nor are essence and actual being other; nor in Him is composition of genus and difference; nor of subject and accident; thus it is manifest that God is in no way composite, but is wholly simple.
Second, because every composite is posterior to its components, and depends on them. But God is first being, as shown above.
Third, because every composite has a cause, since things diverse in themselves do not come together in one thing except through some cause joining them together. But God does not have a cause, as shown above, because He is first efficient cause.
Fourth, because in every composite there should be the actual and the potential, which is not in God, because either one part is actual with respect to the other, or at least all parts are potential with respect to the whole.
Fifth, because every composite is a thing not conjoined to its parts; and this is manifest in whole of dissimilar parts, for no part of man is man, nor is any part of a foot the foot. But in wholes of similar parts, something said of the whole is said of the part, as part of air is air and of water, water; yet something is said of the whole that is not conjoined to its parts, for if the whole water is two cubits, a part is not. Thus in every composite there is something that is not itself. But even if this could be said of what has form, that it has something that is not itself (as in what is white there is something that does not pertain to the notion of white), nonetheless in the form itself there is nothing other than itself. Therefore, because God is form itself, or rather being itself, He cannot be composite in any way. And Hilary touches on this reason (Trin. VII), saying, God, who is power, is not constituted by the weak, nor is He who is light put together from the dark.
To the first, therefore, it must be sad that whatever is from God imitates Him as the caused the first cause. But it belongs to the notion of the caused that it be in some way composed, because at minimum its actual being is other than that which is, as will appear below.
To the second, it must be said that with us the composite is better than the simple because completeness of good for a creature is not found in one simple thing, but in many. But the completeness of divine good is found in one simple thing, as shown below.
