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6.
Coming from a nautical background, I believe this term to be derived in part from the days of the 'men of war', or sailing vessels. I currently don't recall the name of the relatively infamous skipper who used the phrase, but what it refers to is the quarter of a ship -- the port and starboard sides aft, just forward of the transom.

The cannons on these fighting ships were usually placed along the sides, the stern section housing officer quarters. So, to say you will give or show no quarter, is to basically say you will not allow the ass end of your vessel to line up with the guns of your foe. Such condition would leave your vessel most vulnerable.

It is interesting how I used the word quarters to describe the officer berths above. This made me think, as I'm sure the meaning of this term also implies "take no prisoners". This same meaning could easily have come from the days of sail as well.
The Captain exulted, "I WILL SHOW YEE NO QUARTER!", as the salvo of cannon shot bore through his enemy's waterline.
by thirtythreecents November 30, 2006
 
1.
To show no mercy. Refuse to give an opponent the oppurtunity to quit or rest. This use of quarter is probably derived from the meaning of quarter which refers to shelter, as in head quarters. Thus, no quarter means that your opponent is offered no retreat to shelter or protection.
"I shall give no quarter." Said the first dueller.
"None given or asked." Replied his opponent.
by Jason Warren October 26, 2003
 
2.
1. To show no mercy.
2. A badass song by Led Zeppelin.
1. "I'll fight you, when I'm ready"
"Fuck that, I shall show No Quarter"
*Punches person in the face*
2. I am listening to No Quarter by Led Zeppelin.
by Tredmond April 22, 2005
 
3.
In a duel, giving quarter would be to allow an adversary to get back on his feet or recover his weapon. Duels without quarter would not include this often time-consuming practice, allowing a contender to kill an enemy under most condiditons.
Judge: "In this fight, no quarter will be given!"
n00b: "Oh $hit!"
by massive_wordage October 26, 2003
 
4.
To have no refuge. To have no place to go.
There is no quarter from this rain!
by Jason Cook October 26, 2003
 
5.
A respectable hustler does not accept loose change, only bills
I won't take no quarters from you, damn crackhead!
by Papa_ December 06, 2007
 
7.
1. Taking a 1/2 a semester off college
I ain't got no quarter this time 'round. I ain't gittin' no financial aid.
by Idezyne4u October 27, 2003