Tradition says that “Philip, the father of Alexander,
meeting with great difficulties in the siege of Byzantium, set the
workmen to undermine the walls, but a crescent moon discovered the
design, which miscarried; consequently the Byzantines erected a statue
to Diana, and the crescent became the symbol of the state.”
Another legend is that Othman, the Sultan, saw in a vision a
crescent moon, which kept increasing till its horns extended from east
to west, and he adopted the crescent of his dream for his standard,
adding the motto, “Donec repleat orbem.”
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894