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Vine's Expository Dictionary of NT Words [1]

1: (Strong'S #2228 — particle — e — ay )

is a disjunctive particle. One of its uses is to distinguish things which exclude each other, or one of which can take the place of another. It is translated "either" in  Matthew 6:24;  12:33;  Luke 16:13;  Acts 17:21;  1—Corinthians 14:6 . The RV rightly omits it in  Luke 6:42 , and translates it by "or" in  Luke 15:8;  Philippians 3:12;  James 3:12 .

 John 19:18 Revelation 22:2Hence.

King James Dictionary [2]

E'ITHER, a. or pron.

1. One or another of any number. Here are ten oranges take either orange of the whole number, or take either of them. In the last phrase, either stands as a pronoun or substitute. 2. One of two. This sense is included in the foregoing.

Lepidus flatters both,

Of both is flattered but he neither loves,

Nor either cares for him.

3. Each every one separately considered.

On either side of the river.  Revelation 22

4. This word, when applied to sentences or propositions, is called a distributive or a conjunction. It precedes the first of two or more alternatives, and is answered by or before the second, or succeeding alternatives.

Either he is talking, or he is pursuing, or he is on a journey, or perhaps he sleepeth.  50Kings 18.

In this sentence, either refers to each of the succeeding clauses of the sentence.

Webster's Dictionary [3]

(1): ( a. & pron.) Each of two; the one and the other; both; - formerly, also, each of any number.

(2): ( a. & pron.) One of two; the one or the other; - properly used of two things, but sometimes of a larger number, for any one.

(3): ( conj. Either) precedes two, or more, coordinate words or phrases, and is introductory to an alternative. It is correlative to or.

International Standard Bible Encyclopedia [4]

ē´thẽr , ı̄´thẽr  : Often in the sense still common, "one or the other" ( 1 Chronicles 21:21;  Matthew 6:24 , etc.), but also in the obsolete sense of "both" or "each" ( Leviticus 10:1;  1 Kings 7:15;  John 19:18;  Revelation 22:2 ), or in place of (Revised Version) "or" ( Luke 6:42;  Luke 15:8;  Philippians 3:12;  James 3:12 ).