Finishing the God is one argument this week. Many words, but boy do they flow. If you’ve been following the discussion, this should be a breeze. But if not, review the subjects of essence and existence, and recall the in God they are the same.
Chapter 42 That God is One Two (as in Part two)
 Furthermore, given two gods that are posited as agreeing in the necessity of being, either that in which they differ is in some way required for the completion of their necessity of being, or it is not. If it is not, then it is something accidental, because that which accrues to a thing without contributing to its being is an accident. Hence, this accident has a cause, which is, consequently, either the essence of the necessary being or something else. If its essence, then, since the necessity itself of being is its essence, as is evident from what was said above, the necessity of being will be the cause of that accident. But the necessity of being is found in both gods. Therefore, both will have that accident, and thus will not be distinguished with reference to it. If, however, the cause of the accident is something else, it follows that, unless that something else existed, this accident would not exist; and unless this accident existed, the aforesaid distinction would not exist. Therefore, unless that something else existed, these two supposed necessary beings would not be two but one. Therefore, the proper being of each depends on the other, and thus neither of them is through itself a necessary being…
 It is, therefore, not possible to posit many beings of which each is through itself a necessary being.
Notes In other words, it isn’t and can’t be turtles all the way down, which each one giving something to another which the other doesn’t have.
 What is more, if there are two gods, either the name God is predicated of both univocally, or equivocally. If equivocally, this is outside our present purpose. Nothing prevents any given thing from being equivocally named by any given name, provided we admit the usage of those who express the name. But if it be used univocally, it must be predicated of both according to one notion, which means that, in notion, there must be in both one nature. Either, therefore, this nature is in both according to one being, or according to a being that is other in each case. If according to one, there will not be two gods, but only one, since there cannot be one being for two things that are substantially distinguished. If each has its own being, therefore in neither being will the quiddity be its being. Yet this must be posited in God, as we have proved. Therefore, neither of these two beings is what we understand by the name God. It is, therefore, impossible to posit two gods…
Notes Shorter version: since God’s existence and essence are one, as previously proved, to say there are two (or more) gods is to speak equivocally.
 …therefore there cannot be several beings of which each is a necessary being. It is, consequently, impossible that there be several gods.
 Furthermore, either the nature signified by the name God is individuated through itself in this God, or it is individuated through something else. If through something else, composition must result. If through itself, then it cannot possibly belong to another, since the principle of individuation cannot be common to several, It is impossible, therefore, that there be several gods.
 If, again, there are several gods, the nature of the godhead cannot be numerically one in two of them. There must, therefore, be something distinguishing the divine nature in this and in that god. But this is impossible, because, as we have shown above, the divine nature receives the addition neither of essential differences nor of accidents. Nor yet is the divine nature the form of any matter, to be capable of being divided according to the division of matter. It is impossible, therefore, that there be two gods.
Notes Of course, this follows even if you’re not yet convinced God exists. And if you are not yet convinced, you need to go back and re-read especially Chapter 13. And the material proving God is pure act, actuality only, and in Him there is no potential or accidents (if you like, parts that are not essential).
 Then, too, the proper being of each thing is only one. But God is His being, as we have shown. There can, therefore, be only one God…
 Furthermore, we notice in each genus that multitude proceeds from some unity. This is why in every genus there is found a prime member that is the measure of all the things found in that genus. In whatever things, therefore, we find that there is an agreement in one respect, it is necessary that this depend upon one source. But all things agree in being. There must, therefore, be only one being that is the source of all things. This is God.
 Again, in every rulership he who rules desires unity. That is why among the forms of rulership the main one is monarchy or kingship. So, too, for many members there is one head, whereby we see by an evident sign that he to whom rulership belongs should have unity. Hence, we must admit that God, Who is the cause of all things, is absolutely one…
Notes This is St Thomas being complete. I don’t think these last arguments are convincing on their own.  relies on earlier material on being-in-act, and where that ultimately arises.  seems to be missing premises about what God is up to. But, of course, we don’t need either of these two and have enough both from last week and this to prove (with certainty) there is only one God who is the ground of all being, the Unmoved Mover, etc.