The other verb lie once also had an identical variant form, from Old English belicgan, which meant "to encompass, beleaguer," and in Middle English was a euphemism for "to have sex with" (i.e. "to lie with carnally").
"speak falsely, tell an untruth for the purpose of misleading," late 12c., from Old English legan, ligan, earlier leogan "deceive, belie, betray" (class II strong verb; past tense leag, past participle logen), from Proto-Germanic *leuganan (source also of Old Norse ljuga, Danish lyve, Old Frisian liaga, Old Saxon and Old High German liogan, German lügen, Gothic liugan), a word of uncertain etymology, with possible cognates in Old Church Slavonic lugati, Russian luigatĭ; not found in Latin, Greek, or Sanskrit. Emphatic lie through (one's) teeth is from 1940s.
"pretense, false or fanciful representation," 1811, from the verbal phrase make believe, which was used in children's talk by 1773 for "pretend;" see make (v.) + believe. As an adjective, "unreal, sham, pretended," by 1824. The noun form make-belief (1833) was "Substituted by some writers for MAKE-BELIEVE; the formation of the latter, being misunderstood, was imagined to be incorrect" [OED].
Let's-pretend (n.) in the same sense is attested by 1904 (the verbal phrase is from 1848). To make believe (v.) in the sense "cause to believe" is from late 14c.
late 12c., bileave, "confidence reposed in a person or thing; faith in a religion," replacing Old English geleafa "belief, faith," from West Germanic *ga-laubon "to hold dear, esteem, trust" (source also of Old Saxon gilobo, Middle Dutch gelove, Old High German giloubo, German Glaube), from *galaub- "dear, esteemed," from intensive prefix *ga- + PIE root *leubh- "to care, desire, love." The prefix was altered on analogy of the verb believe. The distinction of the final consonant from that of believe developed 15c.
The be-, which is not a natural prefix of nouns, was prefixed on the analogy of the vb. (where it is naturally an intensive) .... [OED]
Meaning "conviction of the truth of a proposition or alleged fact without knowledge" is by 1530s; it is also "sometimes used to include the absolute conviction or certainty which accompanies knowledge" [Century Dictionary]. From c. 1200 as "a creed, essential doctrines of a religion or church, things held to be true as a matter of religious doctrine;" the general sense of "That which is believed" is by 1714. Related: Beliefs.
Belief meant "trust in God," while faith meant "loyalty to a person based on promise or duty" (a sense preserved in keep one's faith, in good (or bad) faith, and in common usage of faithful, faithless, which contain no notion of divinity). But faith, as cognate of Latin fides, took on the religious sense beginning in 14c. translations, and belief had by 16c. become limited to "mental acceptance of something as true," from the religious use in the sense of "things held to be true as a matter of religious doctrine."
Old English belyfan "to have faith or confidence" (in a person), earlier geleafa (Mercian), gelefa (Northumbrian), gelyfan (West Saxon), from Proto-Germanic *ga-laubjan "to believe," perhaps literally "hold dear (or valuable, or satisfactory), to love" (source also of Old Saxon gilobian "believe," Dutch geloven, Old High German gilouben, German glauben), ultimately a compound based on PIE root *leubh- "to care, desire, love" (see belief).
Meaning "be persuaded of the truth of" (a doctrine, system, religion, etc.) is from mid-13c.; meaning "credit upon the grounds of authority or testimony without complete demonstration, accept as true" is from early 14c. General sense "be of the opinion, think" is from c. 1300. Related: Believed (formerly occasionally beleft); believing.
The form beleeve was common till 17c., the spelling then changed, 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. 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.