To finish Aladdin's Window—i.e. to attempt to complete something begun by a great genius, but left imperfect. The genius of the lamp built a palace with twenty-four windows, all but one being set in frames of precious stones; the last was left for the sultan to finish; but after exhausting his treasures, the sultan was obliged to abandon the task as hopeless.
Tait's second part of Dryden's Absalom and Achitophel is an Aladdin's Window.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894