Etymology
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V 
In Middle English, -u- and -v- were used interchangeably, though with a preference for v- as the initial letter (vnder, vain, etc.) and -u- elsewhere (full, euer, etc.). The distinction into consonant and vowel identities was established in English by 1630, under influence of continental printers, but into 19c. some dictionaries and other catalogues continued to list -u- and -v- words as a single series.

No native Anglo-Saxon words begin in v- except those (vane, vat, vixen) altered by the southwestern England habit of replacing initial f- with v- (and initial s- with z-). Confusion of -v- and -w- also was a characteristic of 16c. Cockney accents.

As a Roman numeral, "five." In German rocket weapons systems of World War II, it stood for Vergeltungswaffe "reprisal weapon." V-eight as a type of motor engine is recorded from 1929 (V-engine is attested from 1909), so called for the arrangement. The V for "victory" hand sign was conceived January 1941 by Belgian politician and resistance leader Victor de Laveleye, to signify French victoire and Flemish vrijheid ("freedom"). It was broadcast into Europe by Radio België/Radio Belgique and popularized by the BBC by June 1941, from which time it became a universal allied gesture.
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vac 
1709 as a colloquial shortening of vacation (n.); 1942 as a colloquial shortening of vacuum (v.); 1974 as a colloquial shortening of vacuum cleaner.
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vacancy (n.)
1570s, "a vacating;" c. 1600, "state of being vacant," from Late Latin vacantia, from Latin vacans "empty, unoccupied," present participle of vacare "be empty," from PIE *wak-, extended form of root *eue- "to leave, abandon, give out." From 1690s as "a vacant office or post;" meaning "available room at a hotel" is recorded from 1953. Related: Vacance (1530s); vacancies.
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vacant (adj.)

c. 1300, "not filled, held, or occupied," from Old French vacant "idle, unoccupied" (of an office, etc.), from Latin vacantem (nominative vacans), "empty, unoccupied," present participle of vacare "be empty" (from PIE *wak-, extended form of root *eue- "to leave, abandon, give out"). Meaning "characterized by absence of mental occupation" is from 1570s. Related: Vacantly.

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vacate (v.)
1640s, "to make void, to annul," from Latin vacatus, past participle of vacare "be empty, be void," from PIE *wak-, extended form of root *eue- "to leave, abandon, give out." Meaning "to leave, give up, quit" (a place) is attested from 1791. Related: Vacated; vacating.
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vacation (n.)

late 14c., "freedom from obligations, leisure, release" (from some activity or occupation), from Old French vacacion "vacancy, vacant position" (14c.) and directly from Latin vacationem (nominative vacatio) "leisure, freedom, exemption, a being free from duty, immunity earned by service," noun of state from past-participle stem of vacare "be empty, free, or at leisure," from PIE *wak-, extended form of root *eue- "to leave, abandon, give out."

Meanings "state of being unoccupied," "process of vacating" in English are early 15c. Meaning "formal suspension of activity, time in which there is an intermission of usual employment" (in reference to schools, courts, etc.) is recorded from mid-15c. As the U.S. equivalent of what in Britain is called a holiday, it is attested from 1878.

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vacation (v.)
1866, from vacation (n.). Related: Vacationed; vacationing.
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vaccinate (v.)
1803, "to inoculate with a vaccine," originally with cowpox for the purpose of procuring immunity from smallpox, back-formation from vaccination. Related: Vaccinated; vaccinating.
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vaccination (n.)

1800, used by British physician Edward Jenner (1749-1823) for the technique he publicized of preventing smallpox by injecting people with the similar but much milder cowpox virus (variolae vaccinae), from vaccine (adj.) "pertaining to cows, from cows" (1798), from Latin vaccinus "from cows," from vacca "cow," a word of uncertain origin. A mild case of cowpox rendered one immune thereafter to smallpox. "The use of the term for diseases other than smallpox is due to Pasteur" [OED].

The earlier 18c. method of smallpox protection in England was by a kind of inoculation called  variolation (from variola, the medical Latin word for "smallpox"). There are two forms of smallpox: a minor one that killed 2% or less of the people who got it, and a virulent form that had about a 30% mortality rate and typically left survivors with severe scarring and often blinded them. Those who got the minor form were noted to be immune thereafter to the worse. Doctors would deliberately infect healthy young patients with a local dose of the minor smallpox, usually resulting in a mild case of it at worst, to render them immune to the more deadly form. Jenner's method was safer, as it involved no smallpox exposure.

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vaccine (n.)
"matter used in vaccination," 1846, from French vaccin, noun use of adjective, from Latin vaccina, fem. of vaccinus "pertaining to a cow" (see vaccination). Related: Vaccinal; vaccinic.
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