Etymology
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Words related to intermit

inter- 
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.
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mission (n.)

1590s, "a sending abroad" (as an agent), originally of Jesuits, from Latin missionem (nominative missio) "act of sending, a dispatching; a release, a setting at liberty; discharge from service, dismissal," noun of action from past-participle stem of mittere "to release, let go; send, throw," which de Vaan traces to a PIE *m(e)ith- "to exchange, remove," also source of Sanskrit methete, mimetha "to become hostile, quarrel," Gothic in-maidjan "to change;" he writes, "From original 'exchange', the meaning developed to 'give, bestow' ... and 'let go, send'."

Meaning "an organized effort for the spread of religion or for enlightenment of a community" is by 1640s; that of "a missionary post or station" is by 1769. The diplomatic sense of "body of persons sent to a foreign land on commercial or political business" is from 1620s; in American English, sometimes "a foreign legation or embassy, the office of a foreign envoy" (1805).

General sense of "that for which one is sent or commissioned" is from 1670s; meaning "that for which a person or thing is destined" (as in man on a mission, one's mission in life) is by 1805. Meaning "dispatch of an aircraft on a military operation" (by 1929, American English) was extended to spacecraft flights (1962), hence, mission control "team on the ground responsible for directing a spacecraft and its crew" (1964). As a style of furniture, said to be imitative of furniture in the buildings of original Spanish missions to western North America, it is attested from 1900.

intermitting (adj.)
"stopping at intervals," 1620s, present-participle adjective from intermit (v.). Related: Intermittingly.
intermissive (adj.)

"not continuous," 1580s, from Latin intermiss-, past-participle stem of intermittere "leave off, leave an interval" (see intermit).