The word originally signifies beginning, and so frequently in New Testament, mostly in the Gospels, Acts, Hebrews, Catholic Epistles, and Apocalypse. From this comes a secondary meaning of sovereignty, dominion, magistracy, as being the beginning or first place of power. So mostly by Paul, as principalities (Rom 8:38); rule (1Co 15:24). Compare Luk 12:11, magistrates; Rev., rulers; and Luk 20:20, power. Rev., rule. A peculiar use of the word occurs at Act 10:11, “the sheet knit at the four corners (ἀρχαῖς);” the corners being the beginnings of the sheet. In this passage the A. V. has adopted the first meaning, beginning, in its rendering first estate. Rev. adopts the second, rendering principality. The Jews regarded the angels as having dominion over earthly creatures; and the angels are often spoken of in the New Testament as ἀρχαί, principalities; as Rom 8:38; Eph 1:21; so that this term would be appropriate to designate their dignity, which they forsook.
Habitation (οἰκητήριον)
Only here and 2Co 5:2.
Everlasting (ἀΐδίοις)
Only here and Rom 1:20. For a longer form ἀείδιος, from ἀεί, always.
Under darkness (ὕπο ζόφον)
Under carries the sense of the darkness brooding over the fallen spirits. On darkness, see on 2Pe 2:4. Compare Hesiod: