My predictions were right: attentions flagged. Yet we have to plow through this material. I recall in a course on “Long-memory time series” sitting through a proof that took four hours (spread over two weeks). The destination was unremarkable and the only way anybody knew to get there was through a dense forest. Here the going is slightly easier, plus our destination a lot more interesting.
Be sure to read at least the last Note.
…A material thing is made intelligible by being abstracted from matter and from material conditions. Wherefore that which by its nature is severed from matter and from material conditions, is by its very nature intelligible. Now every intelligible is understood according as it is actually one with the intelligent: and God is Himself intelligent, as we have proved. Therefore since He is altogether immaterial, and is absolutely one with Himself, He understands Himself most perfectly.
Notes We’re skipping around, but this material is stunningly important for understanding the immateriality of the intellect. Not just of God’s. Ours, too. Our understanding of the essence of material things cannot itself be material. Ask Jack Aubrey would say, “Ain’t you amazed?”
…It is impossible to understand simultaneously several things first and per se: since one operation cannot terminate simultaneously in several things. Now God understands Himself sometimes, as we have proved. Therefore if He understands something else by way of an object understood first and per se, it follows that His intellect is changed from consideration to consideration of that thing. But this thing is less excellent than He. Therefore the divine intellect would be changed for the worse: which is impossible.
Notes Given the premises, I can’t see even ardent atheists not accepting this. Don’t forget the “given the premises” part. Review, review, review.
…For the knowledge of an effect is sufficiently obtained from knowledge of the cause: wherefore we are said to know a thing when we know its cause. Now God by His essence is the cause of being in other things. Since therefore He knows His own essence most fully, we must conclude that He knows other things also.
Notes  1 Poster. Anal. ii. 1. (Aristotle, of course). This one is used in Science, too.
…let us suppose that God is the cause of every being, which is clear to a certain extent from what has been said above, and will be more fully proved further on. Accordingly then there can be nothing in a thing without its being caused by Him indirectly or directly. Now if the cause be known its effect is known. Wherefore all that is in anything whatsoever can be known if God be known as well as all the causes intervening between God and that thing.
Now God knows Himself and all the causes that intervene between Him and any thing whatever. For it has been shown already that He knows Himself perfectly. And through knowing Himself He knows whatever proceeds from Him immediately: and again through knowing this, He knows whatever proceeds therefrom immediately, and so on as regards every intervening cause until the ultimate effect. Therefore God knows whatever is in a thing. Now this is to have proper and complete knowledge of a thing, namely, to know whatever is in a thing, whether common or proper. Therefore God has proper knowledge of things, according as they are distinct from one another.
Notes We are accepting, at least for the sake of argument, that God is the ultimate cause of every being. The rest follows immediately. The first paragraph (as always, I added the break) is succinct. Even if you skip the remaining notes, do read the last.
 Further. Whatever acts by intellect, has knowledge of what it does, as regards the proper idea of the thing done: because the knowledge of the doer appoints the form to the thing done. Now God is cause of things by His intellect: since His being is His act of intelligence, and every thing acts in so far as it is actual. Therefore He knows His effect properly, according as it is distinct from others.
Notes Which reminds us of George Carlin’s defense in a case of bank robbery, “I’m sorry, judge, I just forgot.”
 Moreover. The distinction of things cannot arise from chance, for it has a fixed order. Hence it follows that the distinction among things proceeds from the intention of some cause. But it cannot proceed from the intention of a cause that acts from natural necessity: because nature is determined to one thing, so that nothing that acts from natural necessity can have an intention in relation to several things considered as distinct from one another.
It remains therefore that the distinction among things arises from the intention of a cause endowed with knowledge. Now it would seem proper to an intellect to consider the distinction among things: wherefore Anaxagoras declared that an intellect was the principle of distinction. But taken as a whole the distinction of things cannot proceed from the intention of any second cause, since all such causes are included in the universality of distinct effects. Wherefore it belongs to the first cause, which is of itself distinct from all others, to intend the distinction among all things. Therefore God knows things as distinct….
Notes “The distinction of things cannot arise from chance,” which says it all. The cause must have knowledge, because causes are directed towards an end. As for the rest…
Recapitulation. We started with knowledge our sense impressions gave us: that some things change. Why? Because of some cause. What was the nature of the cause for the per-se here-and-now cause? A First Mover. We proved this First Mover had to be the same for every change. “It” had to have no potentiality, “it” was outside time, i.e. eternal, that this Mover was God. It followed that God’s existence and essence were one, that He had no body or materiality, that God could not be known completely, but was Good, i.e. the basis and definition of Good.
And now, though there are a details to mop up (mostly in characterizing this knowledge), we have finally proved that God knows everything. Omniscience. We assumed Omnipotence, but we have already partly proved that. An amazing string of deductions, no? Yes. We’re moving towards God is Truth, Happiness, and all that. After we mop up the characteristics of God, we prove God is the creator, creating big-bang like, out of nothing (no thing). We look at the soul. And much more!
The best way to review is to scan first the Aquinas’s original writing without my comments. For sticky points, then use my notes.
 Ch. xiii.
 Bk. II., ch. xv.
 Ch. xlvii.
 8 Phys. i. 2; ix. 3.
 Ch. xxviii.
 D. 3. ii. 5.
 Ch. xxviii.
 1 Phys. ix. 3.
 Sum. Th. P. I., Q. xiv., A. 11.
 D. 2. iv. 15.