Engage \En*gage"\, v. i.

1. To promise or pledge one's self; to enter into an obligation; to become bound; to warrant.

How proper the remedy for the malady, I engage not. --Fuller.

2. To embark in a business; to take a part; to employ or involve one's self; to devote attention and effort; to enlist; as, to engage in controversy.

3. To enter into conflict; to join battle; as, the armies engaged in a general battle.

4. (Mach.) To be in gear, as two cogwheels working together.

Source: Webster's Revised Unabridged Dictionary (1913)
 

Engage \En*gage"\, v. t. [imp. & p. p. Engaged; p. pr. & vb. n. Engaging.]

[F. engager; pref. en- (L. in) + gage pledge, pawn. See Gage.]

1. To put under pledge; to pledge; to place under obligations to do or forbear doing something, as by a pledge, oath, or promise; to bind by contract or promise. ``I to thee engaged a prince's word.'' --Shak.

2. To gain for service; to bring in as associate or aid; to enlist; as, to engage friends to aid in a cause; to engage men for service.

3. To gain over; to win and attach; to attract and hold; to draw.

Good nature engages everybody to him. --Addison.

4. To employ the attention and efforts of; to occupy; to engross; to draw on.

Thus shall mankind his guardian care engage. --Pope.

Taking upon himself the difficult task of engaging him in conversation. --Hawthorne.

5. To enter into contest with; to encounter; to bring to conflict.

A favorable opportunity of engaging the enemy. --Ludlow.

6. (Mach.) To come into gear with; as, the teeth of one cogwheel engage those of another, or one part of a clutch engages the other part.

Source: Webster's Revised Unabridged Dictionary (1913)