Green’s Dictionary of Slang

a lavatory.

c.1595		Shakespeare Love’s Labour’s Lost V ii: Your lion, that holds his poll-axe sitting upon a close-stool, will be given to Ajax.
1600		Hospital of Incurable Fooles 6: Adoring Stercutio for a god, no lesse unwoorthily then shamfully constituting him a patron and protector of Ajax and his commodities [N].
1609		Jonson Epicene IV v: A stool were better, sir, of Sir Ajax his invention.
1611		R. Cotgrave Dict. of Fr. and Eng. Tongues n.p.: retraict An aiax, privie, house of office.
1630		J. Taylor ‘Taylors Revenge’ in Works (1869) II 144: And with that Marrow-eating hatefull Inke / I’ll make thee (more than any Ajax) stinke.
1665		J. Cotgrave Eng. Treasury 16: Which (like the glorious ajax of Lincoln’s Inne, I saw in London) laps up naught but filth and excrements [N].
1822		R. Nares Gloss. (1888) 13: ajax. The name of this hero furnished many unsavoury puns to our ancestors [...] Sir John Harington, in 1596, published his celebrated tract, called ‘The Metamorphosis of Ajax’, by which he meant the improvement of a jakes, or necessary, by forming it into what we now call a water-closet, of which Sir John was clearly the inventor.