Etymology
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inauguration (n.)

"ceremonial investiture with office; act of solemnly or formally introducing or setting in motion anything of importance or dignity," 1560s, from French inauguration "installation, consecration," and directly from Late Latin inaugurationem (nominative inauguratio) "consecration," presumably originally "installment under good omens;" noun of action from past-participle stem of inaugurare "take omens from the flight of birds; consecrate or install when omens are favorable," from in- "on, in" (from PIE root *en "in") + augurare "to act as an augur, predict" (see augur (n.)).

INAUGURATIO was in general the ceremony by which the augurs obtained, or endeavoured to obtain, the sanction of the gods to something which had been decreed by man; in particular, however, it was the ceremony by which things or persons were consecrated to the gods .... If the signs observed by the inaugurating priest were thought favourable, the decree of men had the sanction of the gods, and the inauguratio was completed. [William Smith (ed.), "Dictionary of Greek and Roman Antiquities," 1842]
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inaugural (adj.)
1680s, from French inaugural (17c.), from inaugurer "to inaugurate" (14c.), from Latin inaugurare "to inaugurate" (see inauguration). The noun meaning "an inaugural address" is recorded from 1832, American English.
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inaugurate (v.)
"induct into office by formal ceremony," c. 1600, a back-formation from inauguration (q.v.) and also from Latin inauguratus, past participle of inaugurare. The etymological sense is "make a formal beginning or induction into office with suitable ceremonies" (which in ancient Rome included especially the taking of auguries). The earlier verb in English was augur (1540s). Related: Inaugurated; inaugurating; inaugurator.
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