From Summa theologiae I.2.2 arg 2; ad 2:
(Scholastic format in red.)
Objection 2. Further, the essence is the middle term of a demonstration. But we cannot know in what God's essence consists, but solely in what it does not consist; as Damascene says (De Fide Orthodoxa I.4). Therefore we cannot demonstrate that God exists.
Major: If we do not know the middle term of a demonstration, then we cannot make that demonstration.
Minor: We do not know the middle term of a demonstration of God's existence.
Conclusion: Therefore, we cannot demonstrate God's existence.
Proof of the Minor: The middle term of a demonstration is the essence of the minor term (the major term in turn is a necessary attribute of the essence). "God" would be the minor term of a demonstration of God's existence. Therefore, God's essence would be the middle term of a demonstration of God's existence--such that the demonstration would look like this: "God is an X; X's exist; therefore, God exists," where X = God's essence. But we do not know what God's essence consists in (but only what it does not consist in). Therefore.
Reply to Objection 2. When the existence of a cause is demonstrated from an effect, this effect takes the place of the definition of the cause in proof of the cause's existence. This is especially the case in regard to God, because, in order to prove the existence of anything, it is necessary to accept as a middle term the meaning of the word, and not its essence, for the question of its essence follows on the question of its existence. Now the names given to God are derived from His effects; consequently, in demonstrating the existence of God from His effects, we may take for the middle term the meaning of the word "God".
I deny the major of the subjunct [i.e., the major of the "proof of the major"]: In propter quid demonstrations (i.e., demonstrations that proceed from causes to effects), the essence is the middle term; but in quia demonstrations (i.e., those that proceed from effects to cause), the effect is the middle term. The demonstration of God's existence is a quia demonstration. Therefore, in the demonstration of God's existence, the middle term are his effects. And I deny the minor. And I deny the conclusion.