furlough (n.)

Old English læfan "to allow to remain in the same state or condition; to let remain, allow to survive; to have left (of a deceased person, in reference to heirs, etc.); to bequeath (a heritage)," from Proto-Germanic *laibjanan (source also of Old Frisian leva "to leave," Old Saxon farlebid "left over"), causative of *liban "remain" (source of Old English belifan, German bleiben, Gothic bileiban "to remain"), from PIE root *leip- "to stick, adhere."

The Germanic root seems to have had only the sense "remain, continue" (which was in Old English as well but has since become obsolete), which also is in Greek lipares "persevering, importunate." But this usually is regarded as a development from the primary PIE sense of "adhere, be sticky" (compare Lithuanian lipti, Old Church Slavonic lipet "to adhere," Greek lipos "grease," Sanskrit rip-/lip- "to smear, adhere to."

Originally a strong verb (past participle lifen), it early switched to a weak form. Meaning "go away, take one's departure, depart from; leave behind" (c. 1200) comes from notion of "leave behind" (as in to leave the earth "to die;" to leave the field "retreat"). From c. 1200 as "to stop, cease; give up, relinquish, abstain from having to do with; discontinue, come to an end;" also "to omit, neglect; to abandon, forsake, desert; divorce;" also "allow (someone) to go."

Colloquial use for "let, allow" is by 1840, said by OED to be chiefly American English. Not related to leave (n.). To leave out "omit" is from late 15c. To leave (something) alone is from c. 1400; to leave (something) be is from 1825. To leave (something/nothing) to be desired is from 1780. To leave it at that is from 1902. Leave off is from c. 1400 as "cease, desist" (transitive); early 15c. as "stop, make an end" (intransitive).

prefix usually meaning "away, opposite, completely," from Old English for-, indicating loss or destruction, but in other cases completion, and used as well with intensive or pejorative force, from Proto-Germanic *fur "before, in" (source also of Old Norse for-, Swedish för-, Dutch ver-, Old High German fir-, German ver-); from PIE *pr-, from root *per- (1) "forward," hence "in front of, before, toward, near, against." Ultimately from the same root as fore (adv.), and compare ver-.

In verbs the prefix denotes (a) intensive or completive action or process, or (b) action that miscarries, turns out for the worse, results in failure, or produces adverse or opposite results. In many verbs the prefix exhibits both meanings, and the verbs frequently have secondary and figurative meanings or are synonymous with the simplex. [ Middle English Compendium]

Probably originally in Germanic with a sense of "forward, forth," but it spun out complex sense developments in the historical languages. It is disused as a word-forming element in Modern English.

From its use in participles it came to be an intensive prefix of adjectives in Middle English (for example Chaucer's forblak "exceedingly black"), but all these now seem to be obsolete.

It is grievous to think how much less careful the English have been to preserve than to acquire. Why have we lost, or all but lost, the ver or for as a prefix,— fordone, forwearied, &c.; and the zer or to,— zerreissen, to rend, &c. Jugend, Jüngling : youth, youngling ; why is that last word now lost to common use, and confined to sheep and other animals? [Coleridge, "German Language," in "Omniana"]

Proto-Indo-European root meaning "to care, desire, love."

It forms all or part of: belief; believe; furlough; leave (n.) "permission, liberty granted to do something;" leman; libido; lief; livelong; love; lovely; quodlibet.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit lubhyati "desires," lobhaya- "to make crazy;" Persian ahiftan "to be tangled, be hit down, be in love;" Latin lubet, later libet "pleases," libido, lubido "desire, longing; sensual passion, lust;" Old Church Slavonic l'ubu "dear, beloved," ljubiti, Russian ljubit' "to love;" Lithuanian liaupsė "song of praise;" Old English lufu "feeling of love; romantic sexual attraction," German Liebe "love," Gothic liufs "dear, beloved."