Etymology
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moonrise (n.)

"rising of the moon, appearance of the moon above the horizon," 1728, from moon (n.) + rise (n.). Verbal noun moon-rising is from late 14c. Browning used moonset (1845) but it seems to be rare.

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menses (n.)
"monthly discharge of blood from the uterus," 1590s, from Latin menses, plural of mensis "month" (see moon (n.)).
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moonwalk (n.)

1966, "a walking on the moon," from moon (n.) + walk (n.). As a dance move in which the dancer  moves backward while appearing to walk forward it was popularized 1983 by Michael Jackson. 

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blue moon (n.)

"a long time," 1821, often in phrases indicating something rarely occurring. Compare at the Greek calends (from an ancient Roman phrase alluding to the fact that the Greeks had nothing corresponding to the Roman calends), and the native in the reign of Queen Dick and Saint Geoffrey's Day "Never, there being no saint of that name," reported in Grose (1788). Nevermass "date which never comes" is from 1540s. Blue moon is suggested earliest in this couplet from 1528:

Yf they say the mone is blewe,
We must beleve that it is true.

Though this might refer to calendrical calculations by the Church. Thus the general "rareness" sense of the term is difficult to disentangle from the specific calendrical one (commonly misinterpreted as "second full moon in a calendar month," but actually a quarterly calculation). In either case, the sense of blue here is obscure. Literal blue moons do sometimes occur under extreme atmospheric conditions.

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menstrual (adj.)

late 14c., "pertaining to menses of females," from Old French menstruel and directly from Latin menstrualis "monthly," especially "of or having monthly courses," from menstruus "of a month, every month, monthly, pertaining to a month," from mensis "month" (see moon (n.)). Occasionally, in astronomy, "monthly" (1590s).

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trimester (n.)

1821, "period of three months," from French trimestre (early 17c.), from Latin trimestris "of three months," from tri- "three" (see tri-) + mensis "month" (see moon (n.)). Specific obstetrics sense is attested from 1900. Related: Trimestrial.

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menstruous (adj.)

"having the monthly flow or discharge," early 15c., from Old French menstrueus and directly from Medieval Latin *menstruosus, from Latin menstruum "of or belonging to menstruation," from menstruus (adj.) "that happens every month, monthly," from mensis "month" (see moon (n.)).

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meniscus (n.)

"a crescent or crescent-shaped body," 1690s in reference to lenses convex on one side, concave on the other, and thicker in the middle; c. 1812 in reference to liquid surfaces, Modern Latin meniscus, from Greek meniskos "lunar crescent," diminutive of mene "moon" (see moon (n.)). Related: Meniscoid; mensicoidal; mensical; mensicate.

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menarche (n.)

"first appearance of menstruation," 1896, from German menarche (1895), from Greek men (genitive menos) "month" (see moon (n.)) + arkhē "beginning" (verbal noun of arkhein "to be the first;" see archon).

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menstruation (n.)

"the period of menstruation," 1680s, from past-participle stem of Late Latin menstruare, from menstruus "monthly" (from mensis "month;" see moon (n.)) + -ation. Old English equivalent was monaðblot "month-blood." Middle English had menstrue (n.), late 14c., from Old French menstrue, from Latin menstruum.

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