"taking a direct object" (of verbs), 1570s (implied in transitively), from Late Latin transitivus (Priscian) "transitive," literally "that may pass over (to another person)," from transire "go or cross over" (see transient).
A relation R is transitive if x R y & y R z => x R z. Equivalence relations, pre-, partial and total orders are all transitive.