It is thou, O king - It is a representation of thyself. Compare Daniel 2:38.
That art grown and become strong - Referring to the limited extent of his dominion when he came to the throne, and the increase of his power by a wise administration and by conquest.
For thy greatness is grown - The majesty and glory of the monarch had increased by all his conquests, and by the magnificence which he had thrown around his court.
And reacheth unto heaven - An expression merely denoting the greatness of his authority. The tree is said to have reached unto heaven Daniel 4:11, and the stateliness and grandeur of so great a monarch might be represented by language which seemed to imply that he had control over all things.
And thy dominion to the end of the earth - To the extent of the world as then known. This was almost literally true.