Actually, it was under Alexander the Great! He was King of Macedonia, one of the many states of Grecia, and under his power ALL of Grecia was united, along with Egypt, Asia Minor, Babylonia, Syria, Persia, Medes, and even into India. When Alexander abruptly died (and who doesn't really?) at the peak of his power, his generals split his Kingdom into FOUR parts.
Two of these four parts, Ptolemy's Egypt and Seleucus Babylonia and Syria, would vex Judea greatly for the next two-three centuries until the rise of the Romans.
Daniel would definitely want the Jews to know what was to become, and it did EXCATLY as his visions and the Angel Gabriel told him it would.
Meant to add, that the Ptolemic Empire of Egypt, and the Seleucid Empire of Syria/Babylonia, would become the Kings of the South and North, respectively, mentioned so much in Daniel Chapter 11.