"that point, place, or state which is halfway between extremes;" c. 1300, originally in music, "a tone intermediate between two other tones," from Old French meien "middle, means, intermediary," noun use of adjective from Late Latin medianus "of or that is in the middle," from Latin medius "in the middle," from PIE root *medhyo- "middle."
The modern range of senses in English mostly appeared late 14c.: "course of action; method, way of attaining an end" (as in ways and means;by means of; by all means; by no means); also "the golden mean, moderation;" and "something physically between two extremes." The mathematical sense, "a quantity having a value intermediate between the values of other quantities, the average obtained by adding several quantities together and dividing the sum by their number" is from mid-15c. Some senses reflect confusion with mean (adj.1).
"intend, have in mind;" Middle English mēnen, from Old English mænan "intend (to do something), plan; indicate (a certain object) or convey (a certain sense) when using a word," from Proto-West Germanic *menjojanan (source also of Old Frisian mena "to signify," Old Saxon menian "to intend, signify, make known," Dutch menen, German meinen "think, suppose, be of the opinion"), from PIE *meino- "opinion, intent" (source also of Old Church Slavonic meniti "to think, have an opinion," Old Irish mian "wish, desire," Welsh mwyn "enjoyment"), perhaps from root *men- (1) "to think."
From late 14c. as "have intentions of a specified kind" (as in to mean well). Of a person or thing, "to be of some account, to matter (to)," by 1888. Conversational question you know what I mean? attested by 1834.
c. 1200, mēne, "shared by all, common, general," a sense now obsolete, shortened from imene, from Old English gemæne "common, public, general, universal, shared by all," from Proto-Germanic *ga-mainiz "possessed jointly" (source also of Old Frisian mene, Old Saxon gimeni, Middle Low German gemeine, Middle Dutch gemene, Dutch gemeen, German gemein, Gothic gamains "common"), from PIE *ko-moin-i- "held in common," a compound adjective formed from collective prefix *ko- "together" (Proto-Germanic *ga-) + *moi-n-, suffixed form of PIE root *mei- (1) "to change; exchange." Compare second element in common (adj.), a word with a sense evolution parallel to that of this word.
Meaning "of common or low origin, inferior in rank or status" (of persons) is attested from early 14c. Sense of "ordinary, inferior in attainment or skill" is from late 14c. Also from late 14c. as "poor in quality, of little value," though this sense survived longer in American than in England. James Stirling, in "Letters from the Slave States" [London, 1857], mentioning mean whites (poor whites in the South who do manual labor and are looked down on by the slaves) notes, " 'Mean' is an Americanism for 'poor,' 'shabby.' They speak here of a 'mean' hotel, a 'mean' dinner, &c."
The pejorative sense of "without dignity of mind, destitute of honor, low-minded" is from 1660s; the specific sense of "stingy, niggardly" is recorded by 1755; the weaker sense of "disobliging, pettily offensive" is from 1839, originally American English slang. All these developments of the English word were furthered by its coincidence in form with mean (adj.2) "middle, middling," which also was used in disparaging senses, and OED notes that some usages of mean it cites "might be referred almost equally to the native and to the foreign adj.; the truth is probably that they are of mixed ancestry."
The inverted sense of "remarkably good" (as in plays a mean Rhythm Master) first recorded c. 1900, perhaps from phrase no mean _______ "not inferior" (1590s, also, "not average," reflecting further confusion with mean (adj.2.)).
mid-15c., "of, pertaining to, or determined by the sun," from Latin solaris "of the sun," from sol "sun" (from PIE root *sawel- "the sun"). Meaning "living room on an upper story" (also sollar) is from Old English, from Latin solarium (see solarium). For "of or proceeding from the sun," the earlier word was Old English sunlic, Middle English sonneli. Solific (1550s) also has been used.
The meaning "operated by means of the sun or its heat" is from 1740; solar power is attested from 1915, solar cell as a photovoltaic device from 1955, solar panel, designed to absorb the sun's rays, is from 1964. The astronomical solar system "sun and the bodies revolving round or dependent on it" is attested from c. 1704; solar wind is so called from 1958.
Solar plexus (1771) "complex of nerves in the pit of the stomach," apparently so called from its central position in the body (see plexus).
"calculate an arithmetical mean," 1882, from mean (n.).
"occupying a middle or intermediate place;" mid-14c., of persons, "of middle rank" (but this is possibly from, or mixed with, mean (adj.1)); from Anglo-French meines (plural), Old French meien, variant of moiien "mid-, medium, common, middle-class" (12c., Modern French moyen), from Late Latin medianus "of the middle," from Latin medius "in the middle" (from PIE root *medhyo- "middle").
From late 14c. as "in a middle state, between two extremes." Meaning "intermediate in time, coming between two events or points in time" is from mid-15c. (the sense in meanwhile, meantime). The mathematical sense "intermediate in a number of greater or lesser values, quantities, or amounts" is from late 14c.
Old English dæg "period during which the sun is above the horizon," also "lifetime, definite time of existence," from Proto-Germanic *dages- "day" (source also of Old Saxon, Middle Dutch, Dutch dag, Old Frisian di, dei, Old High German tag, German Tag, Old Norse dagr, Gothic dags), according to Watkins, from PIE root *agh- "a day." He adds that the Germanic initial d- is "of obscure origin." But Boutkan says it is from PIE root *dhegh- "to burn" (see fever). Not considered to be related to Latin dies (which is from PIE root *dyeu- "to shine").
Meaning originally, in English, "the daylight hours;" it expanded to mean "the 24-hour period" in late Anglo-Saxon times. The day formerly began at sunset, hence Old English Wodnesniht was what we would call "Tuesday night." Names of the weekdays were not regularly capitalized in English until 17c.
From late 12c. as "a time period as distinguished from other time periods." Day-by-day "daily" is from late 14c.; all day "all the time" is from late 14c. Day off "day away from work" is attested from 1883; day-tripper first recorded 1897. The days in nowadays, etc. is a relic of the Old English and Middle English use of the adverbial genitive.
All in a day's work "something unusual taken as routine" is by 1820. The nostalgic those were the days is attested by 1907. That'll be the day, expressing mild doubt following some boast or claim, is by 1941. To call it a day "stop working" is by 1919; earlier call it a half-day (1838). One of these days "at some day in the near future" is from late 15c. One of those days "a day of misfortune" is by 1936.