5 Again the ram was lifted up and exalted, and pushed with its horns towards the west, and towards the north, and towards the south, and humbled many beasts. And they could not stand before him, until the he-goat came from the west and smote the ram and broke his horns and humbled the ram completely. But the ram was the King of Media and Persia, that is, Darius; and the he-goat was Alexander, the son of Philip, the Macedonian. For Daniel saw the ram when he was in the East before the gate of Shushan the fortress that is in the province of Elam, upon the river Ulai.
And he was pushing towards the West and towards the North and towards the South. And none of the beasts could stand before him</em>. And the he-goat of the goats came up from the region of the Greeks, and exalted himself against the ram. And he smote him and broke both his horns, the greater and the lesser. And why did he say that he broke both his horns? Clearly because he humbled both the kingdoms which he ruled; the lesser, that of the Medes, and the greater, that of the Persians.
But when Alexander the Greek came, he slew Darius, King of Media and Persia. For thus the angel said to Daniel, when he was explaining the vision to him:— The ram that you saw was the King of Media and Persia, and the he-goat the King of the Greeks. Now, from the time that the two horns of the ram were broken, until this time, there have been six hundred and forty-eight years.
Source: Demonstrations (New Advent)