Looks like there's some idea of balance between successive sections, then: the secondary meanings in the first section are balanced out by the primary meanings in the second section, and drawing a rune bigger means "getting more of" all of its meanings. And the successive sections tend to get smaller because they're balancing their large-numbered primary meanings against the secondary meanings in the previous section. Does that same principle seem to hold for the other diagrams? 

Yes!

By the time she's done verifying this, she's torn the paper and her hair is a mess. But she's finally getting somewhere! 

. . . Not quite far enough to actually try drawing a diagram of her own, mind you. But somewhere. Is that textbook back in at the library when she goes to return the history books?

Yes, there it is.

Excellent! What's it called? What's in it?

It's called Runecasting and it's a really old book apparently published in the sixties. It confirms her guess that the successive sections are cancellations.

She punches the air and hisses "yes!" right there at the library checkout desk, then laughs at herself.

"Yes?" asks the librarian.

"I had a theory about how some stuff worked that the last book didn't explain, and the book says I was right. This stuff is the most interesting puzzle I've ever seen! And I should probably be reading somewhere other than standing right at your desk, I guess."

The librarian smiles. "As long as you don't try to cast anything, I don't mind if you read in the library, dear."

Margaret giggles. "Okay then." She moves out of the way a bit in case someone else wants to check books in or out, but goes on leaning on the desk and reading.

The librarian doesn't object and processes other checkouts every now and then.

In between checkouts, Margaret remarks, "It would be cool to meet the last person who checked this book out. I don't really know a lot of other critters, and nobody who's into magic."

"I can't give out patron information, but if you want to leave a slip of paper with your number in the book for the next person I won't mind a bit."

"That's a good idea, thanks!" She puts a slip of notebook paper with "Hi fellow magic nerd! Let's meet up!" and then her phone number between two pages and goes back to reading. What else does the book have to say, besides that successive sections are cancellations?

You should never incant in your native language, but ideally you should be fluent and not stumble over the words in the language because stopping incanting, or incanting incorrectly, is a very, very bad idea and can kill you. Diagrams work once. Here's how to circumscribe layers of cancellation; here's how small an effect has to be before it doesn't matter (different between effects; you don't want any extra fire). If you wind up overshooting a cancellation and winding up with a negative amount of a thing, that can have effects that differ per kind of effect - some are fine like that, others you have to get neater.

This . . . this could be enough to actually try a spell. At least if there's anything in here about what the incantations should actually say. She can't actually hold a conversation in French in real time, but individually composed and rehearsed sentences with precise meaning and correct grammar should be doable with a dictionary and patience.

The incantations need to be longish, a sentence or two, not just a word. They should fill in all the gaps about what your spell should do that aren't covered by the fairly simplistic rune meanings. If possible, poetic language seems to help a little where it doesn't sacrifice precision or fluency.

Excellent. Her first actual spell, which is going to be tomorrow at the earliest, is going to be the invisibility diagram from the textbook and an incantation of her own devising. Unless this textbook has exercises in it, or a recommendation for what to do first, anyway.

It does not recommend doing spells just to do spells, since spells are so dangerous.

If this textbook does not understand concepts like "doing simple things for careful practice before attempting the thing you actually want to do" or "doing things for the sake of knowledge", that's, well, it's the sort of mistake you wouldn't expect from a good textbook. But it's what she's got, and she'll probably spend the whole day minus meal breaks taking careful notes on it.

It does recommend drawing out diagrams, leaving them alone for a week, and then checking them over to find out how they would have killed you!

See, that's excellent, that's the sort of exercise a textbook should have in it. There are other things she wants to try before that, like analyses of all the presumably professional-quality diagrams she has access to in this book and the other one, and getting incantations down, but that's definitely a good idea.

She has a total of 7 complete diagrams. They are for:

- invisibility
- water control
- a shield spell
- a space warping spell
- healing
- sleep
- boiling water

and none of them have incantations.

Boiling water is probably the safest of those, if she starts with a small quantity of water in a safe container and is careful to specify that only the water in the container should be affected. Invisibility is potentially safer, except potentially getting stuck invisible with no way to get visible again sounds worse than getting scalded and more likely than boiling her own eyeballs. What does the book have to say about spell sizes--duration, amount of material affected, area of effect, etc--and how to make them larger or more importantly smaller?