Yours, Etc.: Origins and Uses of 8 Sign-Offs
c.1300, "to bend or bow toward," from Old French encliner, from Latin inclinare "to cause to lean; bend, incline, turn, divert," from in- "into, in, on, upon" (see in- (2)) + clinare "to bend," from PIE *klei-n-, suffixed form of *klei- "to lean" (see lean (v.)). Metaphoric sense of "have a mental disposition toward" is early 15c. in English (but existed in classical Latin). Related: Inclined; inclining.
c.1600, "mental tendency," from incline (v.). The literal meaning "slant, slope" is attested from 1846.