"a determining," legal term, from French terminer "to end," in Old French "to decide, rule on," from Latin terminare "to mark the end or boundary," from terminus "end, limit" (see terminus; also see oyer).
1550s, "goal, end, final point," from Latin terminus (plural termini) "an end, a limit, boundary line," from PIE *ter-men- "peg, post," from root *ter-, base of words meaning "peg, post; boundary, marker, goal" (source also of Sanskrit tarati "passes over, crosses over," tarantah "sea;" Hittite tarma- "peg, nail," tarmaizzi "he limits;" Greek terma "boundary, end-point, limit," termon "border;" Gothic þairh, Old English þurh "through;" Old English þyrel "hole;" Old Norse þrömr "edge, chip, splinter"). "The Hittite noun and the usage in Latin suggest that the PIE word denoted a concrete object which came to refer to a boundary-stone." [de Vaan]
In ancient Rome, Terminus was the name of the deity who presided over boundaries and landmarks, focus of the important Roman festival of Terminalia (held Feb. 23, the end of the old Roman year). The meaning "either end of a transportation line" is first recorded 1836.
early 15c., "a criminal hearing of causes," from Anglo-French oyer, Old French oir, oier, from Latin audire "to hear" (from PIE root *au- "to perceive"). Especially in phrase oyer and terminer (early 15c., but from late 13c. in Anglo-Latin and Anglo-French), literally "a hearing and determining," in England a court of judges of assize, in some U.S. states a higher criminal court.
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Harper, D. (n.d.). Etymology of terminer. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/terminer