E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
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.