Etymology
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Words related to *meg-

acromegaly (n.)
"gigantism due to activity of pituitary after normal growth has ceased," 1886, from French acromégalie, from medical Latin acromegalia, from Greek akron "extremity, highest point, mountain peak, headland," neuter of akros "at the furthest point" (from PIE root *ak- "be sharp, rise (out) to a point, pierce") + megas "great" (fem. megale; from PIE root *meg- "great"). Said in contemporary literature to have been coined 1885 by French physician Dr. Pierre Marie.
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Almagest (n.)
late 14c., title of a treatise on astronomy by Claudius Ptolemy of Alexandria, from Old French almageste (13c.), from Arabic al majisti, from al "the" + Greek megiste "the greatest (composition)," from fem. of megistos, superlative of megas "great" (from PIE root *meg- "great").

Originally titled in Greek Mathematike syntaxis ("Mathematical Composition"), commonly called Megale syntaxis "Great Composition" (Greek megale is the fem. of megas); Arab translators in their admiration altered this. Extended in Middle English to other works on astrology or astronomy,
Charlemagne 
king of the Franks (742-814), literally "Carl the Great," from French form of Medieval Latin Carolus Magnus (see Charles + Magnus).
maestro (n.)

"master of music, great teacher or composer," 1797, from Italian maestro, literally "master," from Latin magistrum, accusative of magister "chief, head, director, teacher," contrastive adjective ("he who is greater") from magis (adv.) "more," from PIE *mag-yos-, comparative of root *meg- "great." Applied in Italian to eminent musical composers. Meaning "conductor, musical director" is short for maestro di cappella (1724), literally "master of the chapel" (compare German kapellmeister).

magisterial (adj.)

1630s, "of or befitting to a master or teacher or one qualified to speak with authority," from Medieval Latin magisterialis "of or pertaining to the office of magistrate, director, or teacher," from Late Latin magisterius "having authority of a magistrate," from magister "chief, director" (see master (n.)).

By 17c. often with a suggestion of "arrogant, imperious, domineering." Meaning "holding the office of a magistrate, proper to a magistrate" is from 1650s (see magistrate). Related: Magisterially.

magistral (adj.)

1570s, "forming part of the accepted course of teaching," a sense now obsolete, from Latin magistralis "of a master," from magister "chief, director" (see master (n.)). Meaning "authoritative; of, pertaining to, or befitting a master" is from c. 1600. In pharmacy, of a remedy, etc., "devised by a physician for a particular case, prepared for the occasion" (c. 1600).

magistrate (n.)
Origin and meaning of magistrate

late 14c., "a civil officer in charge of administering laws," also "office or function of a magistrate," from Old French magistrat, from Latin magistratus "a magistrate, public functionary," originally "magisterial rank or office," from magistrare "serve as a magistrate," from magister "chief, director" (see master (n.)). From late 17c. often meaning "justice of the peace" or other minor officials having criminal jurisdiction.

Magna Carta 

also Magna Charta, 1560s, Medieval Latin, literally "great charter" (of English personal and political liberty). The thing was obtained from King John, June 15, 1215; the name is attested in Anglo-Latin by 1218. See magnate, card (n.).

magnate (n.)

mid-15c., "high official, great man, noble, man of wealth," from Late Latin magnates, plural of magnas "great person, nobleman," from Latin 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 suffixed form of PIE root *meg- "great."

magnitude (n.)

c. 1400, "pre-eminence, magnificence;" early 15c., "greatness of size or extent," from Latin magnitudo "greatness, bulk, size," from magnus "great" (from suffixed form of PIE root *meg- "great") + -tudo, suffix forming abstract nouns from adjectives and participles (see -tude).

Meaning "size, extent," whether great or small is from early 15c. Of stars, "brightness or brilliancy expressed as a number" (now on a logarithmic scale) from 1640s, translating Ptolemy's Greek megethos.