[Penyngton]

There's no royal road to geometry. You just have to keep trying things and keep suffering. Sadly, I'm not familiar with that book or particularly with the topics you've mentioned, so I can't recommend specific books, but this is the basic recipe that I've used to teach myself some amount of mathematics:

Start with a book you want to read. If you get stuck, then buy another book (hopefully aimed at a lower level) on that topic and repeat the process with the new book.

Don't be afraid to read "easy" books. You should probably aim to start reading books where you look at the contents page and think you know 80-90% of the material already. I've wasted a lot of time trying to read books that were above my level. The path of least resistance is longer, but in my experience it pays off.

"Do the exercises" is good advice, but don't be too obsessive about it. Be more obsessive about regularly working on the topic, even if that means skipping exercises or jumping between books (on the same topic). You can often find the answer to an exercise in one book in a different book's presentation of the same topic, or on a website or in a paper. As long as you can integrate these discoveries into your conceptual framework of the subject, that's not cheating, it's success.

Writing things out in a lot of detail and working out examples in a lot of detail in a notebook can really help. This is like designing your own exercises and can be better than doing exercises in a book sometimes.

[Tao3300]

> There's no royal road to geometry.

Come on. This is totally not what OP was asking for. Pithy adages might seem wise and helpful, but you're dismissing the fact that OP very much asked for the work and the hard road. They want to backtrack and fill gaps in their skill, and just want recommendations on the path to take to get there.

[Penyngton]

I'm sorry that the phrase riled you. I didn't intend it to be pithy, but simply to demonstrate that it's well known that what OP is asking for doesn't exist.

> Is there a course or series of courses I can take that can build my math skill level to solve such problems with ease?

It seems to me that this question assumes that there is a "royal road" of courses that will turn him into the mathematician he wants to be, but I don't believe that's the case. The only way to get where he wants to be is through a long and difficult process. And in my comment I tried to give what advice I could, however inadequate.

[Tao3300]

"I'm starting to struggle [how do I get better?]" is a lot different than Ptolemy telling Euclid the Elements is too hard and asking for a shortcut. That much is obvious because OP pretty clearly enjoys the work and wants to do more of it. There are going to be right and wrong ways to go about this.

(Here's where I really go off the rails, but trust that I mean this in the same good humored sense with which I would point out that say, vinegar catches flies better than honey.)

We should also cast doubt on the original quote. One, we only have it according to Proclus, roughly eight centuries after Euclid. Two, Ptolemy I was brilliant in his own right, even among the Diadochi. Three, we don't teach anyone straight from the Elements anymore and have learned a great deal about ways people learn. So while I agree there's no substitute for rigorous practice if you're looking to understand a mathematical concept on an intuitive level, we've certainly found some "highways" since 300 BCE.

[antegamisou]

Not the answer OP was hoping for, but definitely the right one.