To set on a firm basis, to establish (an institution, a principle of action, belief, science… const. on; also in (now only in passive).

To make firm, strengthen, establish (any one in a habit, practice, disposition, etc.).

transitive. To fix into something as a foundation.

transitive. To establish (a person) securely in a position, office, privilege, etc. Also figurative.

To appoint or assign the precise position of; to refer (something) to a definite place, time, etc.; †to appoint or attribute exclusively to (some…