Etymology
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matron (n.)

late 14c., matrone, "married woman," usually one of rank or social respectability and mature years (old enough to be the mother of a family, whether actually so or not), from Old French matrone "married woman; elderly lady; patroness; midwife," and directly from Latin mātrona "married woman, wife, matron," from māter (genitive mātris) "mother" (see mother (n.1)).

Also (15c.) "a married female saint." Sense of "female manager of a school, head nurse in a hospital, etc." is recorded by 1550s.

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Demeter 

in Greek religion, the Olympian goddess of agriculture and useful vegetation, protectress of the social order and of marriage, mother of Persephone, from Greek Dēmētēr; the second element generally given as māter (see mother (n.1)); the first element possibly from da, Doric form of Greek "earth" (see Gaia), but Liddell & Scott find this "improbable" and Beekes writes, "there is no indication that [da] means 'earth', although it has also been assumed in the name of Poseidon." The Latin masc. proper name Demetrius means "son of Demeter."

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metropolitan (n.)

mid-14c., "bishop having general superintendency over other bishops of his province," from Late Latin metropolitanus, from Greek metropolis "mother city" (from which others have been colonized), parent state of a colony," also "capital city," and, in Ecclesiastical Greek, "see of a metropolitan bishop," from meter "mother" (see mother (n.1)) + polis "city" (see polis).

In the early church, the bishop of a municipal capital of a province or eparchy, who had general superintendence over the bishops in his province. In modern Catholic use, an archbishop who has bishops under his authority; in the Greek church still the bishop of a municipal capital of a province, ranking above an archbishop.

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matrix (n.)

late 14c., matris, matrice, "uterus, womb," from Old French matrice "womb, uterus" and directly from Latin mātrix (genitive mātricis) "pregnant animal," in Late Latin "womb," also "source, origin," from māter (genitive mātris) "mother" (see mother (n.1)).

The many figurative and technical senses are from the notion of "that which encloses or gives origin to" something. The general sense of "place or medium where something is developed" is recorded by 1550s; meaning "mould in which something is cast or shaped" is by 1620s; sense of "embedding or enclosing mass" is by 1640s.

The mathematical sense of "a rectangular array of quantities (usually square)" is because it is considered as a set of components into which quantities can be set. The logical sense of "array of possible combinations of truth-values" is attested by 1914. As a verb, in television broadcasting, from 1951.

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matriculate (v.)

1570s, "insert (a name) in a register or official list," especially "to admit (a student) to a college by enrolling his name on the register," from Late Latin matriculatus, past participle of matriculare "to register," from Latin mātricula "public register," diminutive of mātrix (genitive mātricis) "list, roll," also "sources, womb" (see matrix).

The connection of senses in the Latin word seems to be via confusion of Greek mētra "womb" (from mētēr "mother;" see mother (n.1)) and an identical but different Greek word mētra meaning "register, lot" (see meter (n.2)). Evidently Latin mātrix was used to translate both, though it originally shared meaning with only one.

Intransitive sense of "to be entered as a member of a university or college, to become a member of a body or society" is by 1851. Also from late 16c. in English as "to adopt as a child; to naturalize," from the other sense of the Latin word, but these meanings now are obsolete. A list or register of persons belonging to an order, society, etc. was a matricula (1550s), from a diminutive of Latin mātrix. Related: Matriculated; matriculating.

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matter (n.)

c. 1200, materie, "the subject of a mental act or a course of thought, speech, or expression," from Anglo-French matere, Old French matere "subject, theme, topic; substance, content; character, education" (12c., Modern French matière) and directly from Latin materia "substance from which something is made," also "hard inner wood of a tree." According to de Vaan and Watkins, this is from mater "origin, source, mother" (see mother (n.1)). The sense developed and expanded in Latin in philosophy by influence of Greek hylē (see hylo-) "wood, firewood," in a general sense "material," used by Aristotle for "matter" in the philosophical sense. 

The Latin word also is the source of Spanish, Portuguese, and Italian materia, Dutch, German, and Danish materie, vernacular Spanish madera, Portuguese madeira "wood" (compare Madeira). The Middle English word also sometimes was used specifically as "piece of wood."

From c. 1200 as "a subject of a literary work, content of what is written, main theme;" sense of "narrative, tale, story" is from c. 1300. Meaning "physical substance generally" is from mid-14c.; that of "substance of which some specific object is or may be composed" is attested from late 14c. Meaning "piece of business, affair, activity, situation; subject of debate or controversy, question under discussion" is from late 14c. In law, "something which is to be tried or proved," 1530s.

Matter of course "something expected" attested from 1739 (adjectival phrase matter-of-course "proceeding as a natural consequence" is by 1840). For that matter "as far as that goes, as far as that is concerned" is attested from 1670s. What is the matter "what concerns (someone), what is the cause of the difficulty" is attested from mid-15c., from matter in the sense of "circumstance or condition as affecting persons and things." To make no matter to "be no difference to" also is mid-15c., with matter in the meaning "importance, consequence."

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father (n.)
Origin and meaning of father

Old English fæder "he who begets a child, nearest male ancestor;" also "any lineal male ancestor; the Supreme Being," and by late Old English, "one who exercises parental care over another," from Proto-Germanic *fader (source also of Old Saxon fadar, Old Frisian feder, Dutch vader, Old Norse faðir, Old High German fatar, German vater; in Gothic usually expressed by atta), from PIE *pəter- "father" (source also of Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), presumably from baby-speak sound "pa." The ending formerly was regarded as an agent-noun affix.

My heart leaps up when I behold
  A rainbow in the sky:
So was it when my life began;
So is it now I am a man;
So be it when I shall grow old,
  Or let me die!
The Child is father of the Man;
I could wish my days to be
Bound each to each by natural piety.
[Wordsworth, 1802]

The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-." Spelling with -th- (15c.) reflects widespread phonetic shift in Middle English that turned -der to -ther in many words, perhaps reinforced in this case by Old Norse forms; spelling caught up to pronunciation in 1500s (compare mother (n.), weather (n.), hither, gather). As a title of various Church dignitaries from c. 1300; meaning "creator, inventor, author" is from mid-14c.; that of "anything that gives rise to something else" is from late 14c. As a respectful title for an older man, recorded from 1550s. Father-figure is from 1954. Fathers "leading men, elders" is from 1580s.

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motherfucker (n.)

also mother-fucker, by 1956, usually simply an intensive of fucker. It is implied in clipped form mother (with the context made clear) by 1928; motherfucking is by 1906. Abbreviation m.f. (for motherfucking) is in a rendition of soldier talk in Pound's "Pisan Cantos" (1948).

A short time after he returned, appellant drew a six-shooter and told deceased, in a loud tone of voice, that he would shoot his God damn heart out, and called him a mother-fucking son of a bitch. He held his pistol on him a little while, and then put it in his pocket, and stood there some time. [account of Puryear vs. State of Texas in Court of Criminal Appeals of Texas, "The Southwestern Reporter," vol. 98, 1907, p. 258. The homicide at the center of the case took place in Austin, Texas, March 3, 1906]
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novercal (adj.)

"characteristic of or resembling a step-mother," 1620s, from Late Latin novercalis, "of or like a step-mother," also "hostile, violent," from noverca, literally "a new mother," from novus "new" (see new).

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Maia 
Roman goddess of fertility, Latin Maia, literally "she who brings increase," from PIE *mag-ya- "she who is great" (suffixed form of root *meg- "great"). Maia, one of the Pleiades, is from Greek Maia, daughter of Atlas, mother of Hermes, literally "mother, good mother, dame; foster-mother, nurse, midwife," said by Watkins to be from infant babbling (see mamma).
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