Yeah, alright, dessert for dinner. She'll eat plenty of vegetables tomorrow or something. She makes a bit of small talk with the restaurant owners, then it's time to go home and stare at runes a while longer and go to sleep.

Come Monday, she thinks to check if Kevin is still in the same place at lunchtime, i.e. hasn't been hauled off for questioning by the secret dragon double secret police.

Kevin has not been hauled off; there he is hanging out with his friends.

She waves at him but sits with a different random person. No nefarious scheme this time, she just wants innocent chitchat where she won't have to tell any lies.

Random other people are pleased to have her company.

She keeps on spending evenings staring at runes. The meanings of the runes have associated numbers; if she writes in the numbers for a single repeated meaning everywhere a rune with that meaning appears in a diagram, is there any pattern to it? Do uses of a single meaning tend to cluster within the diagram, or be evenly spread around it?

Even spread - one in each section is common, usually a secondary or lesser meaning in the largest section and then a primary meaning in the next section. The numbers vary, but so do the sizes of the runes.

Secondary meanings in section n repeated as primary meanings in section n+1 suggests a sort of cascading effect. Does a rune tend to be bigger when the meaning it's repeating from the previous section has a big number?

Yep.

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.