1.To manage; to conduct; to treat. "(Our) clergy have with violence demeaned the matter."
2.To conduct; to behave; to comport; followed by the reflexive pronoun. "They have demeaned themselves Like men born to renown by life or death." "They answered... that they should demean themselves according to their instructions."
3.To debase; to lower; to degrade; followed by the reflexive pronoun. "Her son would demean himself by a marriage with an artist's daughter." Note: This sense is probably due to a false etymology which regarded the word as connected with the adjective mean.
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