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1. The uppermost edge of a hollow container or natural basin.
2. A projecting rim or edge, especially around the bottom of a hat.
3. Full capacity: "No sooner had the fighting started than the hotel filled to the brim with a most extraordinary collection of people" (George Orwell).
v. brimmed, brim·ming, brims
1. To be full to the brim, often to overflowing: The cup is brimming with chowder.
2. To be abundantly filled or supplied: a monument brimming with tourists; workers brimming with pride.
To fill to the brim.

[Middle English brimme.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
References in classic literature ?
The audience would have gone over to Mr Pancks, as one man, woman, and child, but for the long, grey, silken locks, and the broad- brimmed hat.
The wine-cup brimmed again and again, food was piled up in front of the honoured guest, and the attendant who waited was Death.
Forthwith, slowly going from one officer to the other, he brimmed the harpoon sockets with the fiery waters from the pewter.