Etymology
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loose cannon (n.)

in the figurative sense "wildly irresponsible person, potent person or thing freed from usual restraint," by 1896; in the literal sense an object of dread on old warships; the figurative use probably arose from a celebrated scene in a popular late novel by Victor Hugo:

You can reason with a bull dog, astonish a bull, fascinate a boa, frighten a tiger, soften a lion; no resource with such a monster as a loose cannon. You cannot kill it, it is dead; and at the same time it lives. It lives with a sinister life which comes from the infinite. It is moved by the ship, which is moved by the sea, which is moved by the wind. This exterminator is a plaything. [Victor Hugo, "Ninety Three," 1874]
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fast and loose 
described as "a cheating game played with a stick and a belt or string, so arranged that a spectator would think he could make the latter fast by placing a stick through its intricate folds, whereas the operator could detach it at once." [James O. Halliwell, "Dictionary of Archaic and Provincial Words," 1847]. The figurative sense (1550s) is recorded earlier than the literal (1570s).
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hands down (adv.)

to win something hands down (1855) is from horse racing, from a jockey's gesture of letting the reins go loose in an easy victory.

The Two Thousand Guinea Stakes was not the best contested one that it has been our fortune to assist at. ... [T]hey were won by Meteor, with Scott for his rider; who went by the post with his hands down, the easiest of all easy half-lengths. Wiseacre certainly did the best in his power to spoil his position, and Misdeal was at one time a little vexatious. [The Sportsman, report from April 26, 1840]

Ancient Greek had akoniti "without a struggle, easily," from akonitos (adj.), literally "without dust," specifically "without the dust of the arena."

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