And after thee shall arise another kingdom {s} inferior to thee, and another {t} third kingdom of brass, which shall bear rule over all the earth.

(s) Meaning, the Persians who were not inferior in dignity, power, or riches, but were worse with regard to ambition, cruelty, and every type of vice, showing that the world would grow worse and worse, until it was restored by Christ.

(t) That is, those of the Macedonians will be of brass, not alluding to the hardness of it, but to the vileness with regard to silver.

Wesley's Notes

2:39 Another kingdom - This was that of the Medes and Persians, inferior in time for it lasted not half so long as the Assyrian in prosperity and tranquillity; yet, was this wonderful, rich and large for a time. Third kingdom - This was the Grecian monarchy under Alexander the great, called brass, because coarser than the other. Over all the earth - Alexander marched even to the Indies, and was said to conquer the world.

Jamieson-Fausset-Brown Bible Commentary

39. That Medo-Persia is the second kingdom appears from Da 5:28 and Da 8:20. Compare 2Ch 36:20; Isa 21:2.

inferior-"The kings of Persia were the worst race of men that ever governed an empire" [Prideaux]. Politically (which is the main point of view here) the power of the central government in which the nobles shared with the king, being weakened by the growing independence of the provinces, was inferior to that of Nebuchadnezzar, whose sole word was law throughout his empire.

brass-The Greeks (the third empire, Da 8:21; 10:20; 11:2-4) were celebrated for the brazen armor of their warriors. Jerome fancifully thinks that the brass, as being a clear-sounding metal, refers to the eloquence for which Greece was famed. The "belly," in Da 2:32, may refer to the drunkenness of Alexander and the luxury of the Ptolemies [Tirinus].

over all the earth-Alexander commanded that he should be called "king of all the world" [Justin, 12. sec. 16.9; Arrian, Campaigns of Alexander, 7. sec. 15]. The four successors (diadochi) who divided Alexander's dominions at his death, of whom the Seleucidæ in Syria and the Lagidæ in Egypt were chief, held the same empire.

Matthew Henry's Concise Commentary

2:31-45 This image represented the kingdoms of the earth, that should successively rule the nations, and influence the affairs of the Jewish church. 1. The head of gold signified the Chaldean empire, then in being. 2. The breast and arms of silver signified the empire of the Medes and Persians. 3. The belly and thighs of brass signified the Grecian empire, founded by Alexander. 4. The legs and feet of iron signified the Roman empire. The Roman empire branched into ten kingdoms, as the toes of these feet. Some were weak as clay, others strong as iron. Endeavours have often been used to unite them, for strengthening the empire, but in vain. The stone cut out without hands, represented the kingdom of our Lord Jesus Christ, which should be set up in the kingdoms of the world, upon the ruins of Satan's kingdom in them. This was the Stone which the builders refused, because it was not cut out by their hands, but it is become the head stone of the corner. Of the increase of Christ's government and peace there shall be no end. The Lord shall reign, not only to the end of time, but when time and days shall be no more. As far as events have gone, the fulfilling this prophetic vision has been most exact and undeniable; future ages shall witness this Stone destroying the image, and filling the whole earth.