E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Imposed upon, let in, made to suffer loss. I was terribly bitten in that affair. I suffered great loss. To bite is to cheat or suffer retaliation. Thus, Pope says, The rogue was bit, he intended to cheat, but was himself taken in. The biter bit is the moral of Æsops fable called The Viper and the File; and Goldsmiths mad dog, which, for some private ends, went mad and bit a man, but the biter was bit, for The man recovered of the bite, the dog it was that died.