Etymology
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melancholy (n.)

c. 1300, melancolie, malencolie, "mental disorder characterized by sullenness, gloom, irritability, and propensity to causeless and violent anger," from Old French melancolie "black bile; ill disposition, anger, annoyance" (13c.), from Late Latin melancholia, from Greek melankholia "sadness," literally (excess of) "black bile," from melas (genitive melanos) "black" (see melano-) + khole "bile" (see cholera).

Old medicine attributed mental depression to unnatural or excess "black bile," a secretion of the spleen and one of the body's four "humors," which help form and nourish the body unless altered or present in excessive amounts. The word also was used in Middle English for "sorrow, gloom" (brought on by love, disappointment, etc.), by mid-14c. As belief in the old physiology of humors faded out in the 18c. the word remained with a sense of "a gloomy state of mind," particularly when habitual or prolonged.

The Latin word also is the source of Spanish melancolia, Italian melancolia, German Melancholie, Danish melankoli, etc. Old French variant malencolie (also in Middle English) is by false association with mal "sickness."

When I go musing all alone,
Thinking of divers things fore-known,
When I build castles in the air,
Void of sorrow and void of fear,
Pleasing myself with phantasms sweet,
Methinks the time runs very fleet.
   All my joys to this are folly,
   Naught so sweet as melancholy.
When I lie waking all alone,
Recounting what I have ill done,
My thoughts on me then tyrannise,
Fear and sorrow me surprise,
Whether I tarry still or go,
Methinks the time moves very slow.
   All my griefs to this are jolly,
   Naught so sad as melancholy.
[Robert Burton, from "Anatomy of Melancholy," 17c.]
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chance (n.)

c. 1300, "something that takes place, what happens, an occurrence" (good or bad, but more often bad), especially one that is unexpected, unforeseen, or beyond human control, also "one's luck, lot, or fortune," good or bad, in a positive sense "opportunity, favorable contingency;" also "contingent or unexpected event, something that may or may not come about or be realized," from Old French cheance "accident, chance, fortune, luck, situation, the falling of dice" (12c., Modern French chance), from Vulgar Latin *cadentia "that which falls out," a term used in dice, from neuter plural of Latin cadens, present participle of cadere "to fall," from PIE root *kad- "to fall."

In English frequently in plural, chances. The word's notions of "opportunity" and "randomness" are as old as the record of it in English and now all but crowd out its original notion of "mere occurrence." Meaning "fortuity, absence of any cause why an event should happen or turn out as it does, variability viewed as a real agent" is from c. 1400.

Chance is equivalent to the mathematical concept of probability, which is a precisely measurable factor enabling the accurate prediction of average outcomes over long runs of random events — the longer the run, the more accurate the predictions. Luck is at best a platitude and at worst a superstition. [David Partlett, "A History of Card Games"]

Main chance "probability that offers greatest advantage," hence "thing of most importance" is from 1570s. Mathematical sense "probability, likelihood of a certain outcome" is from 1778, hence the odds-making sense "balanced probability of gain or loss." To stand a chance (or not) is from 1796. To take (one's) chances "accept what happens" (early 14c.) is from the old, neutral sense; to take a chance/take chances is originally (by 1814) "participate in a raffle or lottery or game;" extended sense of "take a risk" is by 1826.

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run (n.)

mid-15c. (earlier ren, late 14c.), "a spell of running, the act of running," from run (v.).

The Old English noun ryne/yrn (early Middle English rine) meant "a flowing, a course, a watercourse;" the modern sense of "small stream" is recorded from 1580s, mostly in Northern English dialect and American English. The sense of "a flowing or pouring, as of liquid" is by 1814. In reference to the action of a school of fish moving together, especially upstream or in-shore, by 1820.

From 1804 as "place where anything runs or may run." The meaning "the privilege of going through or over, free access" is from 1755. In. U.S. baseball, "feat of running around the bases without being put out" by 1856; the sense in cricket is from 1746.

Meaning "continuous stretch" (of something) is from 1670s. That of "continuous use, circulation, or observance" (as in run of luck) is by 1714. The general sense of "a continuous series or succession" has yielded many specific meanings, as "three or more playing cards in consecutive order" (1870). In music, "a rapid succession of consecutive tones," by 1835.

The financial meaning "extraordinary series or rush of demands on a bank, etc." is recorded from 1690s. The market sense of "sustained demand for something" is by 1816.

From 1712 as "a spell of sailing between two ports;" hence also "an excursion trip" (1819); "single trip by a railroad train" (1857); the military aircraft attack sense (as in bombing run) is from 1916. Hence also "a regular round in a vehicle" (as in paper run, milk run, etc.).

In printing, the meaning "total number of copies done in a single period of press-work" is from 1909. In publishing, "set or series of consecutive numbers of a periodical," by 1889.

Meaning "tear in a knitted garment or stocking" is from 1922, probably on the notion of "a failure caused by looseness, weakness, or giving way;" to run had a specialized sense in reference to machinery, "to slip, go awry" (1846), and in reference to lace it meant "to unravel, come undone" (1878). Also compare running stitch "loose, open stitch" (1848).

Phrase a run for one's money "satisfaction for trouble taken" is from 1872 in a figurative sense, from horse racing, where it implied real competition (1841).

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