Etymology
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ides (n.)
"middle day of a Roman month," early 14c., from Old French ides (12c.), from Latin idus (plural) "the ides," a word perhaps of Etruscan origin. In the Roman calendar the eighth day after the nones, corresponding to the 15th of March, May, July, and October; the 13th of other months. "Debts and interest were often payable on the ides" [Lewis].
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complementary (adj.)

1620s, "ceremonious" (a sense now obsolete in this spelling of the word), from complement (n.) + -ary. Sense of "forming a complement, mutually completing each other's deficiencies," is attested by 1794, in reference to the calendar of the French Revolution; in reference to colors which in combination produce white light, by 1814. Earlier in the sense "completing, forming a complement" was complemental (c. 1600).

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almanac (n.)

late 14c., "book of permanent tables of astronomical data," attested in Anglo-Latin from mid-13c., via Old French almanach or directly from Medieval Latin almanachus, a word of uncertain origin and the subject of much speculation. The Latin word is often said to be ultimately from Arabic somehow, but an exact phonological and semantic fit is wanting: OED connects it to a supposed Spanish-Arabic al-manakh "calendar, almanac," which is possibly ultimately from Late Greek almenichiakon "calendar," which itself is said to be of Coptic origin. But the author of English words of Arabic Ancestry makes a detailed case  "that the word almanac was pseudo-Arabic and was generated within the circle of astronomers in Paris in the mid 13th century."

One-year versions, showing correspondence of days of the week and month, ecclesiastical calendars, etc., date from 16c.; "astrological and weather predictions appear in 16-17th c.; the 'useful statistics' are a modern feature" [OED].

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November 
c. 1200, from Old French novembre and directly from Latin November (also Novembris (mensis)), from novem "nine" (see nine). The ninth month of the Roman calendar, which began in March. For -ber see December. In Old English, it was Blotmonað "month of sacrifice," literally "blood-month," the time when the early Saxons prepared for winter by sacrificing animals, which they then butchered and stored for food.
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fiscal (adj.)

1560s, "pertaining to public revenue," from French fiscal, from Late Latin fiscalis "of or belonging to the state treasury," from Latin fiscus "state treasury," originally "money bag, purse, basket made of twigs (in which money was kept)," which is of unknown origin. The etymological notion is of the public purse. The general sense of "financial" (1865, American English) was abstracted from phrases fiscal calendar, fiscal year, etc. Related: Fiscally.

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New Year's Eve 

"evening before the first day of the new year," c. 1300; "þer þay dronken & dalten ... on nwe gerez euen." The Julian calendar began on January 1, but the Christian Church frowned on pagan celebrations of this event and chose the Feast of the Annunciation (March 25) as its New Year's Day. The civic year in England continued to begin January 1 until late 12c., and even though legal documents then shifted to March 25, popular calendars and almanacs continued to begin on January 1. The calendar reform of 1751 restored the Julian New Year in England. New Year's was the main midwinter festival in Scotland from 17c., when Protestant authorities banned Christmas, and continued so after England reverted to Christmas, hence the Scottish flavor ("Auld Lang Syne," etc.). New Year's gathering in public places began 1878 in London, after new bells were installed in St. Paul's.

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Ramadan (n.)

ninth month of the Muslim year, period of the annual thirty-days' fast, 1590s, earlier Ramazan (c. 1500), from Arabic Ramadan (Turkish and Persian ramazan), originally "the hot month," from ramida "be burnt, scorched" (compare Mishnaic Hebrew remetz "hot ashes, embers"). In the Islamic lunar calendar, it passes through all seasons in a cycle of about 33 years, but evidently originally it was a summer month.

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April 
fourth month, c. 1300, aueril, from Old French avril (11c.), from Latin (mensis) Aprilis, second month of the ancient Roman calendar, from a stem of uncertain origin and meaning, with month-name suffix -ilis as in Quintilis, Sextilis (the old names of July and August).

Perhaps based on Apru, an Etruscan borrowing of Greek Aphrodite. Or perhaps *ap(e)rilis "the following, the next," from its place as the second month of the old Roman calendar, from Proto-Italic *ap(e)ro-, from PIE *apo- "away, off" (see apo-; compare Sanskrit aparah "second," Gothic afar "after"). Old folk etymology connected it with Latin aperire "to open."

In English in Latin form from mid-12c.; it replaced Old English Eastermonað, which was named for a fertility goddess (see Easter). Re-spelled in Middle English on Latin model (apprile, first attested late 14c.).
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hecatomb (n.)

1590s, from Latinized form of Greek hekatombe, properly (and literally) "offering of 100 oxen," but generally "a great public sacrifice." It is a compound of hekaton "one hundred," which perhaps is dissimilation of *hem-katon, with hen, neuter of heis "one" + *katon "hundred." The second element is bous "ox" (from PIE root *gwou- "ox, bull, cow"). The first month of the Attic calendar (corresponding to July-August) was Hekatombaion, in which sacrifices were made.

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December (n.)

"twelfth and last (by modern reckoning) month of the calendar, the month of the winter solstice," late Old English, from Old French decembre, from Latin December, from decem "ten" (from PIE root *dekm- "ten"); tenth month of the old Roman calendar, which began with March.

The -ber in four Latin month names is probably from -bris, an adjectival suffix. Tucker thinks that the first five months were named for their positions in the agricultural cycle, and "after the gathering in of the crops, the months were merely numbered."

If the word contains an element related to mensis, we must assume a *decemo-membris (from *-mensris). October must then be by analogy from a false division Sep-tem-ber &c. Perhaps, however, from *de-cem(o)-mr-is, i.e. "forming the tenth part or division," from *mer- ..., while October = *octuo-mr-is. [T.G. Tucker, "Etymological Dictionary of Latin"]

Decembrist, in Russian history in reference to the insurrection against Nicholas I in December 1825, is by 1868 in English, translating Russian dekabrist, from dekabr' "December."

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