The tree was great, and strong: and the height thereof reached unto heaven: the sight thereof was even to the ends of all the earth.

The tree grew, and was strong, and its height reached unto the heavens, and the sight thereof to the end of all the earth.

The tree grew, and was strong, and its hight reached to heaven, and the sight of it to the end of all the earth:

become great hath the tree, yea, strong, and its height doth reach to the heavens, and its vision to the end of the whole land;

And the tree became tall and strong, stretching up to heaven, and to be seen from the ends of the earth:

Crevit, multiplicata est, arbor, et invaluit, et altitudo ejus pertigit, hoc est, et altitudo ejus pertingeret, ad coelos, et conspectus ejus ad extremum totius, vel, universae, terrae.

The tree grew - Or the tree was "great" - רבה rebâh. It does not mean that the tree grew while he was looking at it so as to reach to the heaven, but that it stood before him in all its glory, its top reaching to the sky, and its branches extending afar.
And was strong - It was well-proportioned, with a trunk adapted to its height, and to the mass of boughs and foliage which it bore. The strength here refers to its trunk, and to the fact that it seemed fixed firmly in the earth.
And the height thereof reached unto heaven - To the sky; to the region of the clouds. The comparison of trees reaching to heaven is common in Greek and Latin authors. - Grotius. Compare Virgil's description of Fame.
"Mox sese attollit in auras,
Ingrediturque solo, et caput inter nubila condit." -
"AEn. iv. 176
And the sight thereof to the end of all the earth - It could be seen, or was visible in all parts of the earth. The Greek here for "sight" is κῦτος kutos, "breadth, capaciousness." Herodotus ("Polymnia") describes a vision remarkably similar to this, as indicative of a wide and universal monarchy, respecting Xerxes:
"After these things there was a third vision in his sleep, which the magicians (μάγοι magoi) hearing of, said that it pertained to all the earth, and denoted that all men would be subject to him. The vision was this: Xerxes seemed to be crowned with a branch of laurel, and the branches of laurel seemed to extend through all the earth." The vision which Nebuchadnezzar had here, of a tree so conspicuous as to be seen from any part of the world, was one that would be naturally applied to a sovereign having a universal sway.

The tree grew, and was strong,.... Grew higher and broader, taller and thicker, increased in boughs and branches, and became strong and stable, that no winds nor storms could move it: this shows the increasing power of Nebuchadnezzar, the enlargement of his dominions, and the stability of his empire:
and the height thereof reached unto heaven; higher than any on earth; expressive of his dominion over all nations and people of the earth; or of his ambition of deity itself; and so Saadiah illustrates it by Isaiah 14:14. "I will ascend above the heights of the clouds &c.":
and the sight thereof to the end of the earth: being so high, it was seen afar off; the fame of this great monarch reached to the ends of the earth; the eyes of all were turned to him; some looking upon him with wonder, others with envy.