daughter of Calchas the Grecian priest, was beloved by Troilus, one of the sons of Priam. They vowed eternal fidelity to each other, and as pledges of their vow Troïlus gave the maiden a sleeve, and Cressid gave the Trojan prince a glove. Scarce had the vow been made when an exchange of prisoners was agreed to. Diomed gave up three Trojan princes, and was to receive Cressid in lieu thereof. Cressid vowed to remain constant, and Troïlus swore to rescue her. She was led off to the Grecian's tent, and soon gave all her affections to Diomed —nay, even bade him wear the sleeve that Troilus had given her in token of his love.
As false As air, as water, wind, or sandy earth, As fox to lamb, as wolf to heifer's calf, Pard to the hind, or step-dame to her son; `Yea,' let them say, to stick the heart of false-hood, `As false as Cressid.'
Shakespeare: Troilus and Cressida, iii. 2.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894