Engagement, n.
Etymology: [Cf. F. engagement.]
1. The act of engaging, pledging, enlisting, occupying, or entering into contest.
2. The state of being engaged, pledged or occupied; specif., a pledge to take some one as husband or wife.
3. That which engages; engrossing occupation; employment of the attention; obligation by pledge, promise, or contract; an enterprise embarked in; as, his engagements prevented his acceptance of any office. Religion, which is the chief engagement of our league. Milton.
4. (Mil.)
4 more senses
An action; a fight; a battle. In hot engagement with the Moors. Dryden.
5. (Mach.)
The state of being in gear; as, one part of a clutch is brought into engagement with the other part.
Syn. -- Vocation; business; employment; occupation; promise; stipulation; betrothal; word; battle; combat; fight; contest; conflict. See Battle.
Shades of meaning
Fernald has no entry of its own for engagement; he lists it under battle, contract.
Where he writes about it:
Engagement is a somewhat formal expression for battle; as, it was the commander's purpose to avoid a general engagement. — from battle
All these words involve at least two parties, tho an engagement or promise may be the act of but one. — from contract