believeyoudaoicibaDictYouDict[believe 词源字典]
believe: [OE] Believing and loving are closely allied. Late Old English belēfan took the place of an earlier gelēfan ‘believe’ (with the associative prefix ge-), which can be traced back to a prehistoric West and North Germanic *galaubjan (source also of German glauben ‘believe’). This meant ‘hold dear, love’, and hence ‘trust in, believe’, and it was formed on a base, *laub-, which also produced, by various routes, English love, lief ‘dear’, leave ‘permission’, and the second element of furlough.
=> furlough, leave, lief, love[believe etymology, believe origin, 英语词源]
believe (v.)youdaoicibaDictYouDict
Old English belyfan "to believe," earlier geleafa (Mercian), gelefa (Northumbrian), gelyfan (West Saxon) "believe," from Proto-Germanic *ga-laubjan "to believe," perhaps literally "hold dear, love" (cognates: Old Saxon gilobian "believe," Dutch geloven, Old High German gilouben, German glauben), ultimately a compound based on PIE *leubh- "to care, desire, love" (see belief).

Spelling beleeve is common till 17c.; then altered, perhaps by influence of relieve, etc. To believe on instead of in was more common in 16c. but now is a peculiarity of theology; believe of also sometimes was used in 17c. Related: Believed (formerly occasionally beleft); believing. Expression believe it or not attested by 1874; Robert Ripley's newspaper cartoon of the same name is from 1918. Emphatic you better believe attested from 1854.