In the third year of the reign of king Belshazzar a vision appeared unto me, even unto me Daniel, after that which appeared unto me at the first. Dan 8.1
All the prophecies in Daniel and Revelation are one and same theme centering on the great holy war happening between good and evil. The visions concerning the four kingdoms first appeared in Dan 2 and repeated in Dan 7 also repeats in Dan 8. This time the first kingdom is left out.
In Dan 7 the fourth kingdom was given more specifics and in Dan 8 the fourth kingdom was once again given more importance.
Then I lifted up mine eyes, and saw, and, behold, there stood before the river a ram which had two horns: and the two horns were high; but one was higher than the other, and the higher came up last. I saw the ram pushing westward, and northward, and southward; so that no beasts might stand before him, neither was there any that could deliver out of his hand; but he did according to his will, and became great. Dan 8. 3,4
In this vision Ram is used to represent Medo-Persia. Just like Dan 7 where one side of the bear is higher than the other here one horn is higher than the other. The vision says the Kingdom became GREAT.
5. And as I was considering, behold, an he goat came from the west on the face of the whole earth, and touched not the ground: and the goat had a notable horn between his eyes.  And he came to the ram that had two horns, which I had seen standing before the river, and ran unto him in the fury of his power.  And I saw him come close unto the ram, and he was moved with choler against him, and smote the ram, and brake his two horns: and there was no power in the ram to stand before him, but he cast him down to the ground, and stamped upon him: and there was none that could deliver the ram out of his hand.  Therefore the he goat waxed very great: and when he was strong, the great horn was broken; and for it came up four notable ones toward the four winds of heaven.
An he goat is used to represent Greece. The notable horn is Alexander the great. After his death the kingdom was divided into four smaller kingdoms by his generals Cassander, Lysimachus, Seleucus and Ptolemy. The vision says Greece became VERY GREAT.
9. And out of one of them came forth a little horn, which waxed exceeding great, toward the south, and toward the east, and toward the pleasant land.
Rome was represented by a little horn. No animal is used here to represent it.
The key word which identifies Rome in this verse is the horn became EXCEEDINGLY GREAT. Medo-Persia was Great, Greece was Very Great and Rome was exceedingly great.
Compared to all other kingdoms Rome is longer and exceedingly powerful.
A common mistake many theologians make is with the word ‘out of one of them’. They think the little horn came out of four kingdoms of Greece. The gender of Hebrew word used for one of them points to the four winds of heaven not the four horns. Not reading this verse with the help of original Hebrew word causes them to fail to understand the prophecy.