leaf (v.) Look up leaf at Dictionary.com
"to turn over (the pages of a book)," 1660s, from leaf (n.). Meaning "put forth leaves or foliage" is from 1610s. Related: Leafed; leaved; leafing.
leaf (n.) Look up leaf at Dictionary.com
Old English leaf "leaf of a plant, foliage; page of a book, sheet of paper," from Proto-Germanic *laubaz (source also of Old Saxon lof, Old Norse lauf, Old Frisian laf, Dutch loof, Old High German loub, German Laub "foliage, leaves," Gothic lauf), of uncertain origin, perhaps from PIE *leup- "to peel off, break off" (source also of Lithuanian luobas, Old Church Slavonic lubu "bark, rind").

Related to lodge and lobby; for another PIE root see folio. Extended late 14c. to very thin sheets of metal (especially gold). Compare Lithuanian lapas "leaf," from a root also in Greek lepos "bark," lepein "to peel off." Also applied to flat and relatively broad surfaces, especially of flexible or mounted attachments; meaning "hinged flap on the side of a table" is from 1550s. To turn over a (new) leaf (1590s; 1570s as turn the leaf) "begin a new and better course of life" is a reference to the book sense. Among insects, leaf-hopper is from 1852; leaf-cutter from 1816.