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Hellenistic civilization The conquests of Alexander the Great spread Hellenism immediately over the Middle East and far into Asia. After his death in 323 BC, the influence of Greek civilization continued to expand over the Mediterranean world and W Asia. The wars of the Diadochi marked, it is true, the breakup of Alexander's brief empire, but the establishment of Macedonian dynasties in Egypt, Syria, and Persia (the Ptolemies and the Seleucidae) helped to mold the world of that day into a wider unity of trade and learning.

While the city-states of Greece itself tended to stagnate, elsewhere cities and states grew and flourished. Of these the chief was Alexandria . So great a force did Alexandria exert in commerce, letters, and art that this period is occasionally called the Alexandrian Age, and the end of Hellenistic civilization is generally set at the final triumph of Roman power in Alexandria in the 1st cent. BC Pergamum was also prominent, and there were other cities of influence (e.g., Dura).

adjective

This article is part of the FILE devoted to ancient Greece.

Said of the historical period of the conquest ofAlexander (331-323 BC) to Roman rule (31 BC), characterized by large monarchies and Greek civilization specific.
(larousse Dictionary)

Second, what the text shows is that *even* historians (like Badian) who don't consider the Macedonians to have been "originally Greek", even by the time of Philip II and Alexander III, agree that they were considered Greek later on, during Hellenistic times and by the time of the rise of Rome. Certainly before any irrelevant people decided to connect themselves to them, for example.

The Hellenic Age was AFTER Alexander (see Peter Greens book on it). The point Badian is making is Greeks believed Alexander was Greek AFTER he was dead. In the original text the implication is some centuries after. The follow on from that is – Greeks did not believe Alexander was Greek before then.