Old English leaf "leaf of a plant; page of a book," from Proto-Germanic *laubaz (cf. Old Saxon lof, Old Norse lauf, Old Frisian laf, Dutch loof, Old High German loub, German Laub "foliage, leaves," Gothic lauf), perhaps from PIE *leup- "to peel off, break off" (cf. Lithuanian luobas, Old Church Slavonic lubu "bark, rind"). Extended 15c. to very thin sheets of metal (especially gold). Meaning "hinged flap on the side of a table" is from 1550s.
"to turn over (the pages of a book)," 1660s, from leaf (n.). The notion of a book page also is in the phrase to turn over a (new) leaf (1570s). Related: Leafed; leaved; leafing.
Old English læfan "to let remain; remain; have left; bequeath," from Proto-Germanic *laibijan (cf. Old Frisian leva "to leave," Old Saxon farlebid "left over"), causative of *liban "remain," (cf. Old English belifan, German bleiben, Gothic bileiban "to remain"), from root *laf- "remnant, what remains," from PIE *leip- "to stick, adhere;" also "fat."
The Germanic root has only the sense "remain, continue," 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" (cf. Lithuanian lipti, Old Church Slavonic lipet "to adhere," Greek lipos "grease," Sanskrit rip-/lip- "to smear, adhere to." Seemingly contradictory meaning of "depart" (early 13c.) comes from notion of "to leave behind" (as in to leave the earth "to die;" to leave the field "retreat").
"permission," Old English leafe "leave, permission, license," dative and accusative of leaf "permission," from West Germanic *lauba (cf. Old Norse leyfi "permission," Old Saxon orlof, Old Frisian orlof, German Urlaub "leave of absence"), from PIE *leubh- "to care, desire, love, approve" (see love (n.)). Cognate with Old English lief "dear," the original idea being "approval resulting from pleasure." Cf. love, believe. In military sense, it is attested from 1771.
of a tree. The olive-leaf mentioned Gen. 8:11. The barren fig-tree had nothing but leaves (Matt. 21:19; Mark 11:13). The oak-leaf is mentioned Isa. 1:30; 6:13. There are numerous allusions to leaves, their flourishing, their decay, and their restoration (Lev. 26:36; Isa. 34:4; Jer. 8:13; Dan. 4:12, 14, 21; Mark 11:13; 13:28). The fresh leaf is a symbol of prosperity (Ps. 1:3; Jer. 17:8; Ezek. 47:12); the faded, of decay (Job 13:25; Isa. 1:30; 64:6; Jer. 8:13). Leaf of a door (1 Kings 6:34), the valve of a folding door. Leaf of a book (Jer. 36:23), perhaps a fold of a roll.