Paraphrasing the Summa: First part, Question 3, article 4

Article 4. Whether essence and existence are the same in God?

Is God's Divinity the same as God's Being?

Objection 1. It seems that essence and existence are not the same in God. For if it be so, then the divine being has nothing added to it. Now being to which no addition is made is universal being which is predicated of all things. Therefore it follows that God is being in general which can be predicated of everything. But this is false: "For men gave the incommunicable name to stones and wood" (Wisdom 14:21). Therefore God's existence is not His essence.

The first objection says that God's Divinity is not His Being because,  God is Who Is.  In other words, God is said to be all which exists.  Therefore, nothing can be added to God.  But this is not true because men are forbidden from worshipping created things.  Therefore, God's Divinity does not extend to all beings.  And so, God's Divinity is not the same as His Being.

Objection 2. Further, we can know "whether" God exists as said above (I:2:2); but we cannot know "what" He is. Therefore God's existence is not the same as His essence--that is, as His quiddity or nature.

Objection 2 says that we can know that God exists.  Therefore, we know His Being.  But we our mind can not comprehend God's nature. Therefore, God's Being and God's Divinity, are not the same.

On the contrary, Hilary says (Trin. vii): "In God existence is not an accidental quality, but subsisting truth." Therefore what subsists in God is His existence.

St. Hilary of Poitier, in his book "on the Trinity" says that God is self sufficient (subsisting).   Therefore, God is Divine.  In other words, there is only one God.  Only one Divine Nature.  And that is God's Being.

I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways.

St. Thomas says that in Question 3, Article 3, he proved that God is His own essence because there can only be one Eternal Being.

Now,  he will prove that God is also His own Being.

First, whatever a thing has besides its essence

1.  Whatever a creature has beyond its nature

 must be caused either by the constituent principles of that essence 

must be the result EITHER, of those parts which make up that nature.

(like a property that necessarily accompanies the species--as the faculty of laughing is proper to a man--and is caused by the constituent principles of the species),

For example, laughter is proper to humankind because of his psychological  make up.

Another example might be that man stands erect because of his physical build.

or by some exterior agent--as heat is caused in water by fire.

 OR they might be the result of some outside principle acting upon the creature.  For example, fire causes water to heat up.

Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles.

Therefore, he says, if a creature's being differs from his nature, it is because something in his nature causes this difference or because of an action from an outside principle.

Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused.

But no creature can bring itself into being.   A creature's nature does not have the power to bring itself into being.  His being must be caused by an outside principle.

Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.

But that is not true of God.  Because God is the First Cause of all things.  Therefore, God's Divinity can not differ from His Being.

Secondly, existence is that which makes every form or nature actual; for goodness and humanity are spoken of as actual, only because they are spoken of as existing. Therefore existence must be compared to essence, if the latter is a distinct reality, as actuality to potentiality. Therefore, since in God there is no potentiality, as shown above (Article 1), it follows that in Him essence does not differ from existence. Therefore His essence is His existence.

2 .  Being makes all things real.  Purpose and mankind can be addressed because they are real.  Therefore, being is directly related to nature when the two differ.  As the possibility of something happening is to the reality of that thing happening.  But in God, all is real.  God is not a possibility.  God truly exists and has always existed and will always exist.  Therefore, there is no difference between God's nature and His Being.

Thirdly, because, just as that which has fire, but is not itself fire, is on fire by participation; so that which has existence but is not existence, is a being by participation. But God is His own essence, as shown above (Article 3) if, therefore, He is not His own existence He will be not essential, but participated being. He will not therefore be the first being--which is absurd. Therefore God is His own existence, and not merely His own essence.

All creatures exist because God is real.  And we owe our existence to God's Being.  But God does not owe His Being to anything or anyone.  Therefore, God's divinity is His Being.

Reply to Objection 1. A thing that has nothing added to it can be of two kinds. Either its essence precludes any addition; thus, for example, it is of the essence of an irrational animal to be without reason. Or we may understand a thing to have nothing added to it, inasmuch as its essence does not require that anything should be added to it; thus the genus animal is without reason, because it is not of the essence of animal in general to have reason; but neither is it to lack reason. And so the divine being has nothing added to it in the first sense; whereas universal being has nothing added to it in the second sense.

Objection 1 says that God's nature can not be the same as His Being because God's Being is supposed to be all that exists.  If everything exists in God, then it can not increase.  Yet, we are forbidden from worshipping creatures, therefore God's Divine nature does not extend to all which exists unless it increases.

St. Thomas says that there are two ways in which a nature can forbid increase.

1.  If, by nature, it can't increase.

God's Being can't increase, since by nature, God is all which exists.   And God is Divine, by nature.  Therefore, God's Divinity is the same as His Being.

2.  If, by nature, increase is not required.

God's Being is,  by nature, all which exists, therefore, it does not require to increase.  And God is Divine, by nature.  Therefore, God's Divinity is His Being.

 *To me, this does not answer the question of why we don't worship created things.  So, I'll venture to answer that myself.  

Scripture says that "God is He in whom we live, move and have our being (Acts 17:28)."  Therefore, God, being eternal, sustains all life with His own Being.  But, although we and all other creatures, exist in God, we are not Divine because our nature is different from God's.  Therefore, all creatures are mortal but God is eternal.  And that is why, we don't worship creatures.  Because there is only one Divine Being who is eternal.

Reply to Objection 2. "To be" can mean either of two things. It may mean the act of essence, or it may mean the composition of a proposition effected by the mind in joining a predicate to a subject. Taking "to be" in the first sense, we cannot understand God's existence nor His essence; but only in the second sense. We know that this proposition which we form about God when we say "God is," is true; and this we know from His effects (I:2:2).

Objection #2 says that God's Being and Divinity are different because we can understand the former but not the latter.  St. Thomas says that we can't understand either.  Therefore, the argument is false.

In other words, knowing that God exists is not the same as comprehending the grandeur of His existence.  Therefore, our minds can not fully comprehend anything about God.