The meaning of David, City of in the Bible
(From Easton's Bible Dictionary)

David took from the Jebusites the fortress of Mount Zion. He "dwelt in the fort, and called it the city of David" (I Chronicles 11:7). This was the name afterwards given to the castle and royal palace on Mount Zion, as distinguished from Jerusalem generally (I Kings 3:1; 8:1), It was on the south-west side of Jerusalem, opposite the temple mount, with which it was connected by a bridge over the Tyropoeon valley.

(2) Bethlehem is called the "city of David" (Luke 2:4,11), because it was David's birth-place and early home (I Samuel 17:12).

See more on the meaning of David, City Of in the Bible:
David, City Of {International Standard Bible Encyclopedia}

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