The coincidence that helps the dwarves during their stay at Rivendell is when the moon comes out while Elrond is looking at the map. It has moon runes on it with extra information. This helps them along the journey to get to the treasure.
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The moon comes out while Elrond is looking at the map. It has moon runes on it with additional information. They could only be read when the moon was the same as when they were originally written.
Chapter 17 ('The Clouds Burst') of The Hobbit, covers the Battle of the Five Armies. As is the way of battles, many died, "among the goblin dead lay many men and many dwarves, and many a fair elf that should have lived yet long ages merrily in the wood."Fili and Kili, two of the dwarves in the Company died defending Thorin, their uncle in this battle, though their death was not revealed until Chapter 18. Thorin was mortally wounded in the Battle of the Five Armies, and died shortly after.
Chapter 214 during his fight with Riou.
{| |- | Beorn was off checking up on the story that Gandalf and the dwarves had told him. He returned and told them that he had confirmed the story. Beorn captured a warg and a goblin and after getting information from them he killed them. The warg's skin and the goblin's were mounted on the wall. |}
Which book, which part? There could be several answers, you haven't provided enough info. The first thing that comes to mind are the eagles from the Hobbit ... but there's no way to tell without more info.Gandalf came to their rescue in Chapter 4 using "Glamdring the Foehammer."
Bilbo Baggins is loyal because when the dwarves were captured by the goblins he went back into the horrible, horrible tunnels and look for his friends. He had just made up his mind that it was his duty, and that he must turn back.