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Vine's Expository Dictionary of NT Words [1]

1: Κατωτέρω (Strong'S #2736 — — kato — kat'-o, kat-o-ter'-o )

signifies (a) "down, downwards,"  Matthew 4:6;  Luke 4:9;  John 8:6,8;  Acts 20:9; (b) "below, beneath," of place,  Mark 14:66; the realms that lie below in contrast to heaven,  John 8:23; the earth, as contrasted with the heavens,  Acts 2:19; with heos, "unto,"  Matthew 27:51;  Mark 15:38 . The comparative degree, katotero, "under," is used in  Matthew 2:16 . See Bottom , Under.

King James Dictionary [2]

BENE'ATH, prep.

1. Under lower in place, with something directly over or on, as to place a cushion beneath one often with the sense of pressure or oppression, as to sink beneath a burden, in a literal sense. 2. Under, in a figurative sense bearing heavy impositions, as taxes, or oppressive government.

Our country sinks beneath the yoke.

3. Lower in rank, dignity or excellence as, brutes are beneath man man is beneath angels, in the seale of beings. 4. Unworthy of unbecoming not equal to as, he will do nothing beneath his station or character.

BENE'ATH, adv. In a lower place as, the earth from beneath will be barren.

1. Below, as opposed to heaven, or to any superior region as, in heaven above, or in earth beneath.

Webster's Dictionary [3]

(1): (prep.) Lower in rank, dignity, or excellence than; as, brutes are beneath man; man is beneath angels in the scale of beings. Hence: Unworthy of; unbecoming.

(2): (adv.) Below, as opposed to heaven, or to any superior region or position; as, in earth beneath.

(3): (prep.) Under, in relation to something that is superior, or that oppresses or burdens.

(4): (adv.) In a lower place; underneath.

(5): (prep.) Lower in place, with something directly over or on; under; underneath; hence, at the foot of.

International Standard Bible Encyclopedia [4]

bē̇ - nēth ´: The adverb for "under" ( kátō ). In  John 8:23 , the words "ye are from beneath," suggest hell in contrast to heaven. But the succeeding clause, "ye are of this world," gives the key for the interpretation. Earth, not hell, is expressed, although "that more awful meaning surely is not excluded" (Alford).