Webster's Revised Unabridged Dictionary · 1913

Demean

Demean , transitive verb

[Old French demener to conduct, guide, manage, French se démener to struggle; pref. dé- (Latin de) + mener to lead, drive, carry on, conduct, from Latin minare to drive animals by threatening cries, from minari to threaten. See Menace.]

1.
To manage; to conduct; to treat.
[Our] clergy have with violence demeaned the matter. — Milton
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. — Shakespeare
They answered... that they should demean themselves according to their instructions. — Clarendon
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. — Thackeray

This sense is probably due to a false etymology which regarded the word as connected with the adjective mean.

Demean , noun

[Old French demene. See Demean, transitive verb]

1.
Management; treatment. [Obsolete]
Vile demean and usage bad. — Spenser
2.
Behavior; conduct; bearing; demeanor. [Obsolete]
With grave demean and solemn vanity. — West

Demean , noun

[See Demesne.]

1.
Demesne. [Obsolete]
2.
Resources; means. [Obsolete]
You know How narrow our demeans are. — Massinger