Etymology
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vesper (n.)

late 14c., "the evening star," from Old French vespre "evening, nightfall" (12c., Modern French vêpre), from Latin vesper (masc.), vespera (fem.) "evening star, evening, west," related to Greek hesperos, and ultimately from PIE *uekero- "evening, night" (source also of Armenian gišer, Old Church Slavonic večeru, Polish wieczór, Russian večer, Lithuanian vākaras, Welsh ucher, Old Irish fescor "evening"), perhaps an enlarged form of root *we- "down" (source of Sanskrit avah "down, downward"), thus literally "direction in which the sun sets." Meaning "evening" is attested from c. 1600.

Vespers "sixth canonical hour" is attested from 1610s, from plural of Latin vespera "evening;" the native name was evensong (Old English æfen-sang).

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vespertine (adj.)
c. 1500, "of the evening," from Latin vespertinus "of the evening," from vesper "evening" (see vesper).
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Hesperus 
late 14c., poetic for "the evening star," from Latin Hesperus, from Greek hesperos (aster) "the evening (star)," from PIE *wes-pero- "evening, night" (see vesper). Related: Hesperian. Hence Latin and Greek Hesperia "the land of the west," "applied by the Greeks to Italy, by the Romans to Spain or regions beyond" [Century Dictionary].
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west 

Old English west (adv.) "in or toward the west, in a westerly direction," from Proto-Germanic *west- (source also of Old Norse vestr, Old Frisian, Middle Dutch, Dutch west, Old High German -west, only in compounds, German west), which is of uncertain origin. Perhaps from PIE *wes-, reduced form of *wes-pero- "evening, night" (source also of Greek hesperos, Latin vesper "evening, west;" see vesper). Compare also High German dialectal abend "west," literally "evening." French ouest, Spanish oeste are from English.

As an adjective from late 14c.; as a noun from late 12c. West used in geopolitical sense from World War I (Britain, France, Italy, as opposed to Germany and Austria-Hungary); as contrast to Communist Russia (later to the Soviet bloc) it is first recorded in 1918. West Coast of the U.S. is from 1850; West End of London is from 1776; West Side of Manhattan is from, 1858. The U.S. West "western states and territories" originally (1790s) meant those just west of the Alleghenies; the sense gradually extended as the country grew. To go west "die" was "common during the Great War" [OED, 2nd ed.], perhaps from Celtic imagery or from the notion of the setting sun. In U.S. use, in a literal sense "emigrate to the western states or territories," from 1830.

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