The meaning of Beersheba in the Bible
(From Easton's Bible Dictionary)

well of the oath, or well of seven, a well dug by Abraham, and so named because he and Abimelech here entered into a compact (Genesis 21:31). On re-opening it, Isaac gave it the same name (Genesis 26:31-33). It was a favourite place of abode of both of these patriarchs (Genesis 21:31-33; 22:19; 26:33; 28:10). It is mentioned among the "cities" given to the tribe of Simeon (Joshua 19:2; I Chronicles 4:28). From Dan to Beersheba, a distance of about 144 miles (Judges 20:1; I Chronicles 21:2; II Samuel 24:2), became the usual way of designating the whole Promised Land, and passed into a proverb. After the return from the Captivity the phrase is narrowed into "from Beersheba unto the valley of Hinnom" (Nehemiah 11:30). The kingdom of the ten tribes extended from Beersheba to Mount Ephraim (II Chronicles 19:4). The name is not found in the New Testament. It is still called by the Arabs Bir es-Seba, i.e., "well of the seven", where there are to the present day two principal wells and five smaller ones. It is nearly midway between the southern end of the Dead Sea and the Mediterranean.

See more on the meaning of Beersheba in the Bible:
Beersheba {International Standard Bible Encyclopedia}
Beersheba {Hitchcock's Bible Name}

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