Etymology
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Words related to beleave

be- 

word-forming element of verbs and nouns from verbs, with a wide range of meaning: "about, around; thoroughly, completely; to make, cause, seem; to provide with; at, on, to, for;" from Old English be- "about, around, on all sides" (the unstressed form of bi "by;" see by (prep.)). The form has remained by- in stressed positions and in some more modern formations (bylaw, bygones, bystander).

The Old English prefix also was used to make transitive verbs and as a privative prefix (as in behead). The sense "on all sides, all about" naturally grew to include intensive uses (as in bespatter "spatter about," therefore "spatter very much," besprinkle, etc.). Be- also can be causative, or have just about any sense required. The prefix was productive 16c.-17c. in forming useful words, many of which have not survived, such as bethwack "to thrash soundly" (1550s) and betongue "to assail in speech, to scold" (1630s).

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leave (v.)

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).

belive (v.)
obsolete verb from Old English belifan "remain," intransitive form of belæfan "cause to remain" (see beleave). A general Germanic compound (cognates: Old Saxon bilibhon, Gothic bileiban, Old High German biliban, German bleiben, Dutch blijven). It was confused in early Middle English with beleave and merged into it, which gave beleave two clashing senses ("to leave," also "to remain") which might be why the compound word, the cognate of important verbs in other Germanic languages, was abandoned in English and only leave (v.) remains.
*leip- 
Proto-Indo-European root meaning "to stick, adhere; fat."

It forms all or part of: adipose; beleave; delay; leave (v.); lebensraum; life; liparo-; lipo- (1) "fat;" lipoma; liposuction; lively; live (v.); liver (n.1) "secreting organ of the body;" Olaf; relay.

It is the hypothetical source of/evidence for its existence is provided by: Greek liparein "to persist, persevere," aleiphein "anoint with oil," lipos "fat;" Old English lifer "liver," læfan "to allow to remain."