Etymology
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A.H. 
in Islamic calendrical reckoning, 1788, abbreviation of Medieval Latin Anno Hegirae, "Year of the Hegira," the flight of Muhammad from Mecca in 622 C.E., from which Muslims reckon time; from ablative of annus "year" (see annual (adj.)) + genitive of hegira.
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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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month (n.)

"one-twelfth part of a year; one of the twelve parts into which the calendar year is arbitrarily divided," Old English monað, from Proto-Germanic *menoth- (source also of Old Saxon manoth, Old Frisian monath, Middle Dutch manet, Dutch maand, Old High German manod, German Monat, Old Norse manaðr, Gothic menoþs "month"), which is related to *menon- "moon" (see moon (n.)). Originally the month was the interval between one new moon and the next (a sense attested from late Old English).

Its cognates mean only "month" in the Romance languages, but in Germanic they generally continue to do double duty. The development of the calendrical meaning for words from this root in Greek (mēn) and Latin (mensis) was accompanied by the creation of new words for "moon" (selēnē, luna). The phrase a month of Sundays "a very long time" is from 1832 (roughly 7 and a half months but never used literally).

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computer (n.)

1640s, "one who calculates, a reckoner, one whose occupation is to make arithmetical calculations," agent noun from compute (v.).

Meaning "calculating machine" (of any type) is from 1897; in modern use, "programmable digital electronic device for performing mathematical or logical operations," 1945 under this name (the thing itself was described by 1937 in a theoretical sense as Turing machine). ENIAC (1946) usually is considered the first.

Computer literacy is recorded from 1970; an attempt to establish computerate (adjective, on model of literate) in this sense in the early 1980s didn't catch on. Computerese "the jargon of programmers" is from 1960, as are computerize and computerization.

WASHINGTON (AP) — A New York Congressman says the use of computers to record personal data on individuals, such as their credit background, "is just frightening to me." [news article, March 17, 1968]

Earlier words for "one who calculates" include computator (c. 1600), from Latin computator; computist (late 14c.) "one skilled in calendrical or chronological reckoning."

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