Jamieson, Fausset and Brown on Daniel 8:8

8. when he was strong ... great horn was broken--The empire was in full strength at Alexander's death by fever at Babylon, and seemed then least likely to fall. Yet it was then "broken." His natural brother, Philip Aridoeus, and his two sons, Alexander Ægus and Hercules, in fifteen months were murdered.

four ... toward ... four winds--Seleucus, in the east, obtained Syria, Babylonia, Media, &c.; Cassander, in the west, Macedon Thessaly, Greece; Ptolemy, in the south, Egypt, Cyprus, &c.; Lysimachus, in the north, Thrace, Cappadocia, and the north parts of Asia Minor.