(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.