miter (n.1)

in reference to a type of head-dress, an alternative spelling of mitre (see -re).

in carpentry, "a joint at a 45 degree angle," 1670s, of uncertain origin, perhaps from mitre, via notion of joining of the two peaks of the folded cap. As a verb, to make or join with a miter-joint," from 1731. Related: Mitered. Miter-box is attested from 1670s.