Galadriel's intentions.

[littlemanpoet]

Being a ringbearer, Galadriel's intentions would be bound up with that possession, seems to me. Not only that, her intentions also would have to do with her rulership over Lorien and her care for all Elves and beneficence toward all free peoples. Only Boromir, who brought his own darkness with him into Lorien, saw her as a temptress. The others felt themselves tested rather than tempted. So it seems to me.

Thus, her intentions, I would say, are for the furtherance of the cause of the destruction of the Ring. I think she felt that the Fellowship still had a role to play in helping Frodo get to Mordor, even though she may have had the foresight that it would break. Her intentions therefore seem to me to be to determine how trustworthy to the cause each member of the Fellowship was.

Frodo: hand the Ring to another and give up.
Sam: go back to the Shire.
Pippin: same
Merry: same
Gimli: riches untold
Legolas: to go into the West?
Aragorn: Arwen without the need to prove himself by earning kingship?
Boromir: the Ring, obviously

I'm sure someone could do better than that for speculation.

[the phantom]

Here's some guesses on what Galadriel offered and how the members of the Fellowhip responded. I'll start with the serious ones.

Galadriel: Boromir, Captain of the armies of Gondor, why have you not taken your chance?
Boromir: What chance?
Galadriel: You have the opportunity to garauntee Gondor's victory over Sauron. It's been in front of you since the Council.
Boromir: The Ring.
Galadriel: Yes, the Ring. It is powerful. You are already a great leader of men. Imagine yourself with the Ring lending you strength. None could stand before you, not even Sauron.
Boromir: But Elrond, and Gandalf... they said that it was unwise to use this thing- Isildur's Bane. It has already slain Is...
Galadriel: It slipped from Isildur's finger. That's what caused his death. The lack of it. Had it remained with him, it never would've been called his "bane".
Boromir: But still, the wise ones at the Council said that it was perilous to use.
Galadriel: How would they know? Who has actually used the Ring? Isildur? He was slain not long after the Ring came to him. Gollum? The Ring did not twist him, he was already capable of great evil; the Ring merely unlocked his potential. What about Frodo? He is certainly not corrupt. He is a kind, polite hobbit, with an elvish air about him, and he has possessed this thing for quite a long while. It has not corrupted him. And if not him, how could it possibly corrupt you- a strong-willed, true-hearted man of Gondor?
Boromir: I... I can't just take it. Frodo... he... it's his now.
Galadriel: It only came to him by chance. It could've come to you instead. Don't you think that it should have?
Boromir: I...I... don't know. Maybe I... but, I can't take it from him.
Galadriel: If you don't, then the Ring will be taken right into Sauron's hands. How can anyone hope to enter Mordor unmarked and march past thousands of orcs to the Cracks of Doom? It is folly.
Boromir: It is. But... I can't do anything about that... not now.

Galadriel: Aragorn, you can run away with Arwen into the wilderness and live out your days together in happiness.
Aragorn: And forsake the people of Middle-Earth?
Galadriel: What do you owe them? You've already spent many years laboring for them.
Aragorn: And all in vain if this quest fails. Should not the heir to the throne of men be the first to resist Sauron and the last to abandon the fight? I will do my part in defeating Sauron, or die trying.
Galadriel: Your story and Arwen's- it is so similar to that of Beren and Luthien. Your situation is the same as his. You are faced with a task that is entirely impossible, and yet you rush on, like Beren, towards the impossible instead of allowing yourself rest and peace.
Aragorn: But Beren completed his "impossible" mission.
Galadriel: I only hope you will be as fortunate.
Aragorn: Even if I am not, it is still the right choice.

Galadriel: Frodo, you never should've been placed in this position. This matter is beyond one so small. Go back to your beloved Shire.
Frodo: I'd love to, but... I'd be letting Gandalf, and everyone, down. I just think this is what I'm supposed to do.

Galadriel: Sam, you've been away for too long. You should go back and feast on fried fish and chips. You couldn't say no to that.
Sam: Yes, yes we could. Keep nasssty chips.

Galadriel: Pippin, why are you here? Elrond wasn't too comfortable with letting you tag along. You're probably going to look into a magic seeing stone or something and doom the entire Fellowship. Why don't you head back to the Shire, kick back at the Green Dragon, and order a pint of beer.
Pippin: It comes in pints?

Galadriel: Merry, this quest is very dangerous. You might be mistaken for Frodo and get carried off by orcs, or get called "small rag-tag" by a mean old wizard. Go back to the Shire where it's safe.
Merry: Oh, I suppose you think Witch Kings just kill themselves? I've gotta job to do.

Galadriel: Gimli, if you leave the Fellowship, I'll give you three of my beautiful hairs.
Gimli: What happens if I don't leave?
Galadriel: Um, probably the same thing.
Gimli: Then I'm staying. I'll probably run into more orcs this way. And you did mean h-a-i-r-s, right- not h-a-r-e-s?

Galadriel: Legolas, you don't have to stay with the rest of the group. You can go back to Mirkwood and run around and climb trees and sing instead. Doesn't that sound like fun?
Legolas: Nice offer- till the singing part. I've had it with the Tra-la-la song- we sing it all the time! Worst tune ever to come out of Rivendell. I'd rather stay here with the dwarf than go back to that.

[ninlaith]

That is an extremely good question. I only wish I had the best answer suitable. but i suppose I only have a mock up. I think Galadriel's intentions were of the best kind. However, i believe her motive was to try to 'break" the will of each of them; such as she did to Boromir. She awoke in Boromir, as you say, "a sleeping giant" so perhaps she was testing to see if this giant was withi each of them. If they each had this sleeping giant the quest would inevitably fail. I believe she wanted to test each of them before they went any further in their quest.All the bribing was just to sweeten the deal. She made the temptation even worse with her promises which, evidently, shook the faiths of each of the members of the fellowship. So, all in all, her planned worked and proved to be successful in some cases.

[Thinlómien]

Maybe she tested them and their will, could it be broken through? Could the enemy break thorugh their mind? Do they have strong enough will to be in the fellowship? Are they dangerous to the others? That was maybe what she wanted to find out...?

[littlemanpoet]

I think she showed each one his own heart, and each one was tempted by what had been laid bare.

[Feanor of the Peredhil]

I viewed it much as I view the times when my mother gives me choices. Or not actually *gives* them to me, but shows them to me. Example: Well, either you can take the easy way out and nobody is going to give you a hard time for it, because after all it's your choice, or you can challenge yourself, stick to your word, meet your full potential, and be a success. Your choice.

For all that I've joked about every problem the Fellowship encounters being Galadriel's fault (PM me for explanation, if needed), I picture her as rather benevolent and kind. Although Galadriel couldn't actually give the Fellowship what it seemed she was offering, they could, possibly, give it to themselves. She was testing their hearts and their trueness to the cause of good.

Fea

[Halbarad]

Boromir was correct in saying that Galadriel offered that which she did not have the power to give. All they had to do to get what they desired was

to turn aside from the road and leave the Quest

. I think her reasons for doing this were to temper the individuals, to make them realise why they were really there. Better to do it while they're in a safe place, for they get to think about the choice and make a decision without doing it at a time or in a place where it could jeopardise the Quest. A chain is only as strong as its weakest link, and if she could get the link to crack early, so much the better.