(1):

(adv.) With just deduction of consequence; with right connection of ideas; logically.

(2):

(adv.) By remote consequence; not immediately; eventually; as, to do a thing consequentially.

(3):

(adv.) In a regular series; in the order of cause and effect; with logical concatenation; consecutively; continuously.

(4):

(adv.) With assumed importance; pompously.