word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."
A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
mid-15c., menglen, transitive, "mix, blend, form a combination of, bring (something and something else) together," frequentative of Middle English myngen "to mix," from Old English mengan (related to second element in among), from Proto-Germanic *mangjan "to knead together" (source also of Old Saxon mengian, Old Norse menga, Old Frisian mendza, German mengen), from a nasalized form of PIE root *mag- "to knead, fashion, fit."
The formation may have been suggested by cognate Middle Dutch mengelen. Intransitive sense of "to be or become joined, combined, or mixed" is by 1520s. Of persons, "enter into intimate relation, join with others, be sociable," from c. 1600. Related: Mingled; mingling; minglement.