Etymology
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Words related to *meg-

majuscule (adj.)

1704, of a letter, "capital;" 1738 as a noun, "a capital letter," from French majuscule (16c.), from Latin maiuscula (littera), fem. of maiusculus "somewhat larger, somewhat greater," diminutive of maior (see major (adj.)).

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master (n.)
Origin and meaning of master

late Old English mægester "a man having control or authority over a place; a teacher or tutor of children," from Latin magister (n.) "chief, head, director, teacher" (source of Old French maistre, French maître, Spanish and Italian maestro, Portuguese mestre, Dutch meester, German Meister), contrastive adjective ("he who is greater") from magis (adv.) "more," from PIE *mag-yos-, comparative of root *meg- "great." The form was influenced in Middle English by Old French cognate maistre.

From late 12c. as "man eminently or perfectly skilled in something," also "one who is chief teacher of another (in religion, philosophy, etc.), religious instructor, spiritual guide." Sense of "master workman or craftsman, workman who is qualified to teach apprentices and carry on a trade on his own account" is from c. 1300. The meaning "one charged with the care, direction, oversight, and control of some office, business, etc." is from mid-13c.; specifically as "official custodian of certain animals kept for sport" early 15c. (maister of þe herte houndes; the phrase master of the hounds is attested by 1708). As a title of the head or presiding officer of an institution, late 14c.; as "captain of a merchant vessel" early 14c.

In the broadest sense, "one who has power to control, use, or dispose (of something or some quality) at will," from mid-14c. Also from mid-14c. as "one who employs another or others in his service" (in which sense the correlative word was servant, man, or apprentice); also "owner of a living creature" (a dog, a horse, also, in ancient contexts a slave); paired with slave in the legal language of the American colonies by 1705 in Virginia.

In academic sense "one who has received a specific degree" (translating Medieval Latin magister) it is attested from mid-13c., originally "one who has received a degree conveying authority to teach in the universities;" master's degree, originally a degree giving one authority to teach in a university, is from late 14c.

Also used in Middle English of dominant women. From 1530s as "male head of a household." As a title or term of respect or rank, mid-14c. As a title prefixed to the name of a young gentleman or boy of the better class not old enough to be called Mr., short for young master (late 16c.). Sense of "chess player of the highest class at national or international level" is by 1894. Meaning "original of a recording" is by 1904.

As an adjective from late 12c. Master-key, one that will open ("master") a number of locks so differently constructed that the key proper to each will open none of the others" is from 1570s. Master race "race of people considered to be pre-eminent in greatness or power" (typical in reference to Nazi theories of the Aryan race, perhaps based on German Herrenvolk) is by 1935. From 1530 as "artist of distinguished skill;" old masters is attested by 1733.

Master bedroom, "bedroom designed for the use of the owner of the property," as opposed to bedrooms for children or guests, is by 1919 in U.S. home-builders publications (e.g. Building Age, April 1919).  It seems to be based on the English master's bedroom (by 1903) "bedroom of a headmaster or other master at an English boarding school or other similar institution."

The top floor was treated much the same as the two lower ones. Here the closet was made just a bit larger so as to allow for a bathtub, thus pushing the partition forward, making the front room less deep than the rooms below, yet paradoxically larger, because it takes in the whole front of the house. This is what is known in English advertisements as the "Master's bedroom." [The House Beautiful, June 1921] 
maxim (n.)

early 15c., maxime, "an axiom, statement of a self-evident truth," from Old French maxime, from Late Latin maxima, shortened from phrases such as maxima propositio (Boethius), maxima sententarium "axiom," literally "greatest or chief premise, greatest among propositions" (one which is general and absolute), from fem. of maximus "greatest," from PIE *mag-samo-, superlative form of root *meg- "great."

The modern meaning "summary statement of an established or accepted proposition serving as a rule or guide, a proposition ostensibly expressing some general truth" is from 1590s.

maximum (n.)

"the greatest amount, quantity, or degree," 1740, from French maximum and directly from Latin maximum (plural maxima), neuter of maximus "greatest," which is superlative of magnus "great, large, big" (of size), "abundant" (of quantity), "great, considerable" (of value), "strong, powerful" (of force); of persons, "elder, aged," also, figuratively, "great, mighty, grand, important," from PIE *mag-samo-, superlative form of root *meg- "great."

may (v.2)

"to celebrate May Day, to take part in May Day festivities," late 15c., from May. Maying as "the observance of May Day with all its sports and games" is attested from late 14c. (maiing).

And as a vapour, or a drop of raine
Once lost, can ne'r be found againe:
                     So when or you or I are made
                     A fable, song, or fleeting shade;
                     All love, all liking, all delight
                     Lies drown'd with us in endlesse night.
Then while time serves, and we are but decaying;
Come, my Corinna, come, let's goe a Maying.
[Robert Herrick, "Corinna's Going a-Maying," 1648] 
may (v.1)

Old English mæg "am able" (infinitive magan, past tense meahte, mihte), from Proto-Germanic root *mag-, infinitive *maganan (Old Frisian mei/muga/machte "have power, may;" Old Saxon mag/mugan/mahte; Middle Dutch mach/moghen/mohte; Dutch mag/mogen/mocht; Old High German mag/magan/mahta; German mag/mögen/mochte; Old Norse ma/mega/matte; Gothic mag/magan/mahte "to be able"), from PIE root *magh- "to be able, have power." A present-preterit verb (with can, shall, etc.). Also used in Old English as a "auxiliary of prediction."

mayor (n.)

"principal officer of a municipality, chief magistrate of a city or borough," c. 1300, mair, meir (mid-13c. as a surname), from Old French maire "head of a city or town government" (13c.), originally "greater, superior" (adj.), from Latin maior, major, comparative of magnus "great, large, big" (of size), "abundant" (of quantity), "great, considerable" (of value), "strong, powerful" (of force); of persons, "elder, aged," also, figuratively, "great, mighty, grand, important," from PIE *mag-no-, from root *meg- "great."

Mayoress is attested from late 15c. as "the wife of a mayor;" by 1863 as "woman holding the office of mayor."

mega- 

before vowels meg-, word-forming element often meaning "large, great," but in physics a precise measurement to denote the unit taken a million times (megaton, megawatt, etc.), from Greek megas "great, large, vast, big, high, tall; mighty, important" (fem. megale), from PIE root *meg- "great." Mega began to be used alone as an adjective by 1982.

High-speed computer stores 2.5 megabits [headline in "Electronics" magazine, Oct. 1, 1957]
megalo- 
word-forming element meaning "large, great, exaggerated," from combining form of Greek megas "large, great" (stem megal-), from PIE root *meg- "great."
mickle (adj., n.)

"great, large; much, abundant; a great deal," a dialectal survival of Old English micel, mycel "great, intense, big, long, much, many," from Proto-Germanic *mekilaz (source also of Old Saxon mikil, Old Norse mikill, Old High German mihhil, Gothic mikils), from PIE root *meg- "great." Its main modern form is much (q.v.); the common Middle English form was muchel. The phonetic development of the dialectal survival is obscure and might reflect Old Norse influence. Related: Mickleness. Middle English had muchel-what (pron.) "many various things."

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