How to not be polite. I ended up winning the War.

Can you take second chair and sit next to her? It is either you or she:)

Let her put the stuff first on the table again the next time but sit down first and tell her it's your time now :>
Don't forget the laughter in the end

Stick a piece of gum in the chair! XD

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Perhaps she feels similarly: "this guy almost sniped MY study spot the one day I was a little late"?
If you both feel you have a just claim to the spot, then perhaps you could share a table, an outlet, a floor, a couch, a corner, whatever? Perhaps you'd have to bring over a chair? Either way, you'd do this simply by putting yourself there and minding your own business. I find earplugs/headphones work well.
If sharing won't work after that, then she'll leave or a passive aggressive cold war will break out where you guys try to drive away the other one by taking up space, being loud, etc. Just be prepared for it and ready to be the more passive aggressive one. If she asks you to leave, say, "Oh, that's ok. We can share since the the library's for all of us. Here, I'll move my bag to make some more room for you," then put your headphones back on and go back to studying.
Hopefully it won't come to that and you can share.

You mean there was a place in library that you already was there busy reading and then left there for a moment and when you came back you saw she had taken your place ( The chair ) ?

Learn Kung Fu.

Punch her in the face with a trowel. Then choke her with your elbows while you rub them on her broken teeth.
If you spot the slightest clue on her face that she's about to say something or even to scream, remind her that she's in a library for god's sake.

Alternative :
territorial pissing.

Throw the books on the table faster than her!

or accidentally bump her to spill her things then you put everything on your spot then help her if you feel guilty.

If she gets there first, just call in a bomb threat so you can try again \o/

where is the puzzle? :(

Accidentally drop water on the desk/chair, after she leaves grab the towel you had in your bag and clean the mess -> profit

or pee on her to show dominance :p

or:

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Hmm. If you're there first, drop the books on the table before she does.
If she drops her books first, put yours on the table anyway and smile at her while sitting down. The chair will be yours then.
The thing is to politely force her to speak up first. She'll have to choose between walking way or causing a scene.

If she does cause a scene, you can politely make her look bad which usually works. People don't like being confronted with their own bad behaviour when there's others looking at them.

Or find a new and better spot, for example not in the library but another place.

Is she hot? Maybe you can get a date!

She might just be into you? And is challenging your space to force you to speak to her.
Why not start a chat and see what she's like? :P

Or you know, take the chair and put your books in the bag etc.
And, couldn't you check what her angle was, and take that route before her?

Grab a different chair and share the table, put on headphones and put up the music loud enough so she can hear it as well.

I see the beginning a love story lol. JK
chill, maybe u two would become good friends. it seems to me shes making an effort to annoy you, which is a sign.....
talk to her.

Whip out your penis and act accordingly depending on her reaction:

1. If she laughs hysterically knock her stuff off of the table and take the chair before she recovers.
2. If she looks at it in awe then you may have a keeper and now need to find a bed that you both fit in.
3. If she runs away screaming hysterically then the table is all yours!
4. You'll get arrested and go to jail. They have plenty of places in there that you can sit down at and she won't be there to torment you.

Wear running shoes and try to be faster than her. :B But what if she's doing it on purpose and wants you to talk with her? ;)

It's time to drop the books. This is personal.

Rape her

If it's as you describe, then she's deliberately being unreasonable.
First, try reason-- "actually, I was here first. I was just getting things out of my bag-- don't you see that?" When she smirks or ignores you, try something like, "Yeah, this is a great spot, isn't it? How about if we're both here at 10am, we take turns at this spot?"
Chances are, neither of these will work. At that point, you either abandon the spot and find someplace else (perhaps the seat across from her?), or do your best to make it absolutely clear that you're there first. Leave your 50lbs backpack just outside or inside the library, and make a beeline for the spot with a single textbook in your hands. Wear running shoes. Beat her to the spot, sit down immediately, and open your book and start reading until she leaves. Then leave your book open at the spot and retrieve your bag. If she's sitting there when you return, I think you have grounds to sic the library bouncers on her. :)

Good luck and let us know how it turns out.

I would ask someone else (maybe a friend who could be there a few minutes earlier) to block the spot and then change places with him infront of her.
Or if it really is that close... Just run the next time.

Or the real canadian way (according to southpark) eat some beans and then make her do not want that place anymore, if you know what I mean

Or just make her uncomfortable with remarks "I see you always want to come first, so how about I make you "come" first?". But that could result in Problems I guess ;-> Would be funny for everyone hearing it, though. ;->

As a fellow Canadian I know how it feels.... You smile and are polite while under the skin you just want to pick up the nearest beaver or polar bear or moose or baby seal and club the person with it (specially when they are American and keep asking "please say about, its so cute with your accent").

I know people who know people who might know people and we could frame her.... we could make it look like she stole whats holy to all Canadians..... a barrel of maple syrup. We plant it in her car... well ok strap it to the top of her car cause a barrel is quite large and then call the police. And because she stole that she goes away for life!!!!

See its just a simple plan, nothing can go wrong with it, being Canadians we'll get away with it cause no one will believe we could ever do it, we're too polite to fame someone. Heck even writing about it here can't even get us caught cause no one will believe it!!!

Ohhhh just thought of something worse..... we could strand her in Newfoundland.... she'd never find her way home, cause no one can understand a word that they say so any directions they give she won't be able to understand!!!! And then that perfect study spot will be yours....

As soon as she puts her stuff down...

(╯°□°)╯︵ ┻━┻

Do you guys really have heads cut into two different pieces?