Etymology
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institute (n.)

1510s, "purpose, design," from Latin institutum "an ordinance; a purpose; a custom; precedents; principal components," literally "thing set up," noun use of neuter past participle of instituere "to set up, put in place; arrange; found, establish" (see institute (v.)).

From 1540s in English as "an established law." The sense of "an organization or society devoted to some specific work," especially literary or scientific, is from 1828, from French use in Institut national des Sciences et des Arts (established 1795); Dutch instituut, German Institut also are from French. The specialized (mostly U.S.) sense "traveling academy for teachers in a district" is from 1839.

A "Teachers' Institute" is a meeting composed of teachers of Common Schools, assembled for the purpose of improvement in the studies they are to teach, and in the principles by which they are to govern. It is the design of a Teachers' Institute to bring together those who are actually engaged in teaching Common Schools, or who propose to become so, in order that they may be formed into classes and that these classes, under able instructers, may be exercised, questioned and drilled, in the same manner that the classes of a good Common School are exercised, questioned and drilled. [Horace Mann, secretary's report to the Boston Board of Education, Sept. 1, 1845]
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institute (v.)
early 14c., "to establish in office, appoint," from Latin institutus, past participle of instituere "to set up, put in place; arrange; found, establish; appoint, designate; govern, administer; teach, instruct," from in- "in" (from PIE root *en "in") + statuere "establish, to cause to stand," from PIE root *sta- "to stand, make or be firm." General sense of "set up, found, introduce" first attested late 15c. Related: Instituted; instituting.
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institution (n.)
c. 1400, "action of establishing or founding (a system of government, a religious order, etc.)," from Old French institucion "foundation; thing established" (12c.), from Latin institutionem (nominative institutio) "a disposition, arrangement; instruction, education," noun of state from institutus (see institute (v.)).

Meaning "established law or practice" is from 1550s. Meaning "establishment or organization for the promotion of some charity" is from 1707. Jocular or colloquial use for "anything that's been around a long time" is from 1837.
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*sta- 

*stā-, Proto-Indo-European root meaning "to stand, set down, make or be firm," with derivatives meaning "place or thing that is standing."

It forms all or part of: Afghanistan; Anastasia; apostasy; apostate; armistice; arrest; assist; astatic; astatine; Baluchistan; bedstead; circumstance; consist; constable; constant; constitute; contrast; cost; desist; destination; destine; destitute; diastase; distance; distant; ecstasy; epistasis; epistemology; establish; estaminet; estate; etagere; existence; extant; Hindustan; histidine; histo-; histogram; histology; histone; hypostasis; insist; instant; instauration; institute; interstice; isostasy; isostatic; Kazakhstan; metastasis; obstacle; obstetric; obstinate; oust; Pakistan; peristyle; persist; post (n.1) "timber set upright;" press (v.2) "force into service;" presto; prostate; prostitute; resist; rest (v.2) "to be left, remain;" restitution; restive; restore; shtetl; solstice; stable (adj.) "secure against falling;" stable (n.) "building for domestic animals;" stage; stalag; stalwart; stamen; -stan; stance; stanchion; stand; standard; stanza; stapes; starboard; stare decisis; stasis; -stat; stat; state (n.1) "circumstances, conditions;" stater; static; station; statistics; stator; statue; stature; status; statute; staunch; (adj.) "strong, substantial;" stay (v.1) "come to a halt, remain in place;" stay (n.2) "strong rope which supports a ship's mast;" stead; steed; steer (n.) "male beef cattle;" steer (v.) "guide the course of a vehicle;" stem (n.) "trunk of a plant;" stern (n.) "hind part of a ship;" stet; stoa; stoic; stool; store; stound; stow; stud (n.1) "nailhead, knob;" stud (n.2) "horse kept for breeding;" stylite; subsist; substance; substitute; substitution; superstition; system; Taurus; understand.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit tisthati "stands;" Avestan histaiti "to stand;" Persian -stan "country," literally "where one stands;" Greek histēmi "put, place, cause to stand; weigh," stasis "a standing still," statos "placed," stylos "pillar;" Latin sistere "stand still, stop, make stand, place, produce in court," status "manner, position, condition, attitude," stare "to stand," statio "station, post;" Lithuanian stojuos "I place myself," statau "I place;" Old Church Slavonic staja "place myself," stanu "position;" Gothic standan, Old English standan "to stand," stede "place;" Old Norse steði "anvil;" Old Irish sessam "the act of standing."

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MIT 

originally M.I.T., abbreviation of Massachusetts Institute of Technology, attested from 1892. The school was founded 1861.

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tech (n.)
1906 as short for technical college (or institute, etc.), American English; 1942 as short for technician.
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Gallup poll 
1940, from George H. Gallup (1901-1984), U.S. journalist and statistician, who in 1935 set up the American Institute of Public Opinion.
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Smithsonian 
"Smithsonian Institute," named for English scientist and philanthropist James Smithson (1765-1829), who left a legacy to the U.S. government to found it. The mineral smithsonite also is named for him.
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think tank (n.)
also think-tank, 1959 as "research institute" (first reference is to Center for Behavioral Sciences, Palo Alto, Calif.); it had been colloquial for "the brain" since 1905. See think + tank (n.).
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macadamia (n.)

Australian evergreen tree, commercially important for its edible nut, 1904, from Modern Latin (1858), named for Scotland-born chemist Dr. John Macadam, secretary of the Victoria Philosophical Institute, Australia, + abstract noun ending -ia.

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