Etymology
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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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*eue- 
*euə-, Proto-Indo-European root meaning "to leave, abandon, give out," with derivatives meaning "abandoned, lacking, empty."

It forms all or part of: avoid; devastation; devoid; evacuate; evanescent; vacant; vacate; vacation; vacuity; vacuole; vacuous; vacuum; vain; vanish; vanity; vaunt; void; wane; want; wanton; waste.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit una- "deficient;" Avestan va- "lack," Persian vang "empty, poor;" Armenian unain "empty;" Latin vacare "to be empty," vastus "empty, waste," vanus "empty, void," figuratively "idle, fruitless;" Old English wanian "to lessen," wan "deficient;" Old Norse vanta "to lack."
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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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void (adj.)
c. 1300, "unoccupied, vacant," from Anglo-French and Old French voide, viude "empty, vast, wide, hollow, waste, uncultivated, fallow," as a noun, "opening, hole; loss," from Latin vocivos "unoccupied, vacant," related to vacare "be empty," from PIE *wak-, extended form of root *eue- "to leave, abandon, give out." Meaning "lacking or wanting" (something) is recorded from early 15c. Meaning "legally invalid, without legal efficacy" is attested from mid-15c.
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avoidance (n.)
late 14c., "action of emptying," from avoid + -ance. Sense of "action of dodging or shunning" is recorded from early 15c.; it also meant "action of making legally invalid," 1620s; "becoming vacant" (of an office, etc.), mid-15c.
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are (n.)
metric unit of square measure, 10 meters on each side (100 square meters), 1819, from French, formed 1795 by decree of the French National Convention, from Latin area "vacant piece of ground" (see area).
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hectare (n.)
1817, from French hectare "a hundred ares," formed from Latinized form of Greek hekaton "a hundred" (see hecatomb) + Latin area "vacant piece of ground" (see area). A superficial measure equal to 100 ares, coined by decree of the French National Convention in 1795.
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vague (adj.)

"uncertain as to specifics," 1540s, from French vague "empty, vacant; wild, uncultivated; wandering" (13c.), from Latin vagus "strolling, wandering, rambling," figuratively "vacillating, uncertain," perhaps from PIE *Huog-o-  and cognate with Old Norse vakka "to stray, hover," Old High German wankon "to totter, stagger," Old High German winkan "to waver, stagger, wink," Old English wincian "to nod" [de Vaan]. Related: Vagueness.

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air-space (n.)

also airspace, by 1821 in reference to stove and furnace construction, from air (n.1) + space (n.). From 1852 in reference to the cubic contents of a room (with reference to the persons in it) in sanitary regulations for boarding rooms, hospitals, etc. In firearms, "a vacant space between the powder charge and the projectile" (1847). By 1910 as "portion of the atmosphere controlled by a country above its territory."

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siege (n.)
early 13c., "a seat" (as in Siege Perilous, early 13c., the vacant seat at Arthur's Round Table, according to prophecy to be occupied safely only by the knight destined to find the Holy Grail), from Old French sege "seat, throne," from Vulgar Latin *sedicum "seat," from Latin sedere "to sit," from PIE root *sed- (1) "to sit." The military sense is attested from c. 1300; the notion is of an army "sitting down" before a fortress.
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