Etymology
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minimum (n.)

1660s, "smallest portion into which matter is divisible," a sense now obsolete, from Latin minimum "smallest" (thing), neuter of minimus "smallest, least," superlative of minor "smaller" (from PIE root *mei- (2) "small"). Meaning "smallest amount or degree, least amount attainable" is from 1670s.

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minimum (adj.)

"of the smallest possible amount or degree, that is the lowest obtainable," 1810, from minimum (n.).

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minimize (v.)

"reduce to a minimum, make as little or slight as possible," 1802, first recorded in Bentham; see minimum + -ize. As "to depreciate, treat slightingly," by 1875. Related: Minimized; minimizing.

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mini- 

word-forming element meaning "miniature, minor," abstracted from miniature, with sense perhaps influenced by minimum. The vogue for mini- as a prefix in English word coinage dates from c. 1960; minicam for "miniature camera" (1937) is an early use.

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*mei- (2)

Proto-Indo-European root meaning "small."

It forms all or part of: administer; administration; comminute; diminish; meiosis; Menshevik; menu; metier; mince; minestrone; minim; minimum; minister; ministration; ministry; minor; minuend; minuet; minus; minuscule; minute; minutia; Miocene; mis- (2); mite (n.2) "little bit;" mystery (n.2) "handicraft, trade, art;" nimiety.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit miyate "diminishes, declines;" Greek meion "less, smaller;" Latin minus, minor "smaller," minuere "to diminish, reduce, lessen;" Old English minsian "to diminish;" Russian men'she "less."

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low (n.3)
the low point of anything, the minimum, 1818, originally in card games; general sense by 1911.
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minimal (adj.)

"smallest, least; pertaining to a minimum," 1660s, from Latin minimus "smallest, least" (see minim) + -al (1).

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hyperalgesia (n.)

"abnormal sensitivity to pain," 1854, from hyper- "over, exceedingly, to excess" + ending probably based on analgesia. Related: Hyperalgesic.

Hyperaesthesia, then, is the peculiar state in which the absolute sensibility is increased—the minimum of stimulation needed to excite perception being less than normal. Hyperalgesia is where stimuli which normally cause only a slight sensation give rise to pain in consequence of the lowering of the pain minimum. [The Medical Record, April 1, 1867]
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pianissimo (adv.)

musical instruction, "with the minimum of force or loudness," 1724, from Italian pianissimo "very softly," superlative of piano, which is ultimately is from Latin planus "flat, smooth, even," later "soft" (from PIE root *pele- (2) "flat; to spread").

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quantum (n.)

1610s, "sum, amount," from Latin quantum (plural quanta) "as much as, so much as; how much? how far? how great an extent?" neuter singular of correlative pronominal adjective quantus "as much" (see quantity).

The word was introduced in physics directly from Latin by Max Planck, 1900, on the notion of "minimum amount of a quantity which can exist;" reinforced by Einstein, 1905. Quantum theory is from 1912; quantum mechanics, 1922. The term quantum jump "abrupt transition from one stationary state to another" is recorded by 1954; quantum leap "sudden large advance" (1963), is often figurative.

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