1540s, "divide in two equal parts" (a sense now obsolete), from Latin mediatus, past participle of mediare "to halve," later, "be in the middle," from Latin medius "middle" (from PIE root *medhyo- "middle"); from 1640s as "occupy a middle place or position." Meaning "act as a mediator, intervene for the purpose of reconciliation" is from 1610s; that of "settle by mediation, harmonize, reconcile" is from 1560s, perhaps back-formations from mediation or mediator. Related: Mediated; mediates; mediating.
early 15c., "intermediate," from Medieval Latin mediatus, past-participle adjective from Latin mediare "to be in the middle," from medius "middle" (from PIE root *medhyo- "middle"). Related: Mediately.