E. Cobham Brewer 1810–1897. Dictionary of Phrase and Fable. 1898.

Square the Circle.

To attempt an impossibility. The allusion is to the mathematical question whether a circle can be made which contains precisely the same area as a square. The difficulty is to find the precise ratio between the diameter and the circumference. Popularly it is 3.14159 … . the next decimals would be 26537, but the numbers would go on ad infinitum.