Don't fire until you see the white of their eyes who said it

The answer is William Prescott

William Prescott was an American Colonel in the Revolutionary War who commanded the patriots in the Battle of Bunker Hill. Prescott was in command of 1,200 troops with the order to defend Bunker's Hill and Breed's Hill, both being located near Charleston, South Carolina. At daybreak of June 17, 1775, after the American patriots had finished fortifying each of the positions, the British finally realized the presence of the patriots. After they had become aware of their presence, they launched three assaults on the patriots defending the two positions.
 
After the second assault, the Patriots had started to get a little low on ammo and became a little discouraged in their chances, so William Prescott delivered his famous quote, " Do not fire until you can see the whites of their eyes." 

The third and final assault resulted in the patriots running out of ammo and eventually retreating to Cambridge. Although, the British technically won, they had received heavy losses in their men, which resulted in their being a little more cautious when attacking the American Patriots. The Battle resulted in an approximate 450 Patriot soldiers losing their lives, to the almost 1,100 British who lost their lives in this intense skirmish.

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