Etymology
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vet (v.)
"to submit (an animal) to veterinary care," 1891, from veterinarian. The colloquial sense of "subject (something) to careful examination" (as of an animal by a veterinarian, especially of a horse before a race) is attested by 1901. Related: Vetted; vetting.
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vet (n.2)
1848, shortened form of veteran (n.).
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vetting (n.)
1918, verbal noun from vet (v.).
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fat (n.)
"fat part of anything," mid-14c., from fat (v.). Cognate with Dutch vet, German Fett, Swedish fett, Danish fedt. As a component of animal bodies, 1530s. Figurative sense of "best or most rewarding part" is from 1560s. Expression the fat is in the fire originally meant "the plan has failed" (1560s).
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veteran (n.)
c. 1500, "old experienced soldier," from French vétéran, from Latin veteranus "old, aged, that has been long in use," especially of soldiers; as a plural noun, "old soldiers," from vetus (genitive veteris) "old, aged, advanced in years; of a former time," as a plural noun, vetores, "men of old, forefathers," from PIE *wet-es-, from root *wet- (2) "year" (source also of Sanskrit vatsa- "year," Greek etos "year," Hittite witish "year," Old Church Slavonic vetuchu "old," Old Lithuanian vetušas "old, aged;" and compare wether). Latin vetus also is the ultimate source of Italian vecchio, French vieux, Spanish viejo. General sense of "one who has seen long service in any office or position" is attested from 1590s. The adjective first recorded 1610s.
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veterinarian (n.)

"animal doctor, one who practices the art of treating disease and injuries in domestic animals," 1640s, from Latin veterinarius "of or having to do with beasts of burden," also, as a noun, "cattle doctor," from veterinum "beast of burden," perhaps from vetus (genitive veteris) "old" (see veteran), possibly from the notion of "experienced," or of "one year old" (hence strong enough to draw burdens). Another theory connects it to Latin vehere "to draw," on notion of "used as a draft animal." Replaced native dog-leech (1520s).

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veterinary (adj.)
1791, from Latin veterinarius "of or pertaining to beasts of burden," from veterinus (see veterinarian).
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vetch (n.)

climbing herb, late 14c., from Old North French veche, variant of Old French vece, from Latin vicia "vetch," which perhaps is related to vincire "to bind" (compare second element of periwinkle (n.1)), or from PIE root *weik- (2) "to bend, to wind." Dutch wikke, German Wicke are loan-words from Latin vicia.

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veto (n.)
1620s, from Latin veto, literally "I forbid," first person singular present indicative of vetare "forbid, prohibit, oppose, hinder," of unknown origin. In ancient Rome, the "technical term for protest interposed by a tribune of the people against any measure of the Senate or of the magistrates" [Lewis].
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