gag

The root here (better thought of as gage) comes from Old French gager, 'to pledge, to wager,' itself of Frankish Germanic origin. A gage was something handed over as a guarantee — a pledge, a security, a stake. When you put up a gage, you committed yourself: you were on the hook until the promise was kept. That single idea — binding yourself by a pledge — runs through the whole useful part of this family.

The core of the family is engage. en- (to make, to put into) + gage (pledge) = to put yourself under a pledge, to commit. From that one verb the meanings fan out, all held together by the idea of being bound to something:

- engage = to commit yourself to an activity, to take part with full attention (engage in debate), and also to hire someone (engage a lawyer — you pledge to pay them) or to begin combat (engage the enemy — armies committed to the fight).
- engaged = bound by a pledge. Bound to marry someone → engaged (the wedding pledge). Bound up in work → engaged (busy, occupied). Bound to a task → engaged (deeply involved).
- engagement = the act or state of being pledged: a promise to marry, a fixed appointment, or active involvement.
- engaging = describing something that pledges your attention without your trying — it pulls you in, it holds you.

Reverse the pledge with dis- (apart, undo) and you get disengage: to release yourself from the commitment — pull troops back, withdraw from a conversation, or unhook one gear from another. The image is always the same: a bond being undone.

The original noun gage still survives, mostly in legal and old-fashioned use, meaning a pledge or security (and as the second half of mortgage — literally a 'dead pledge').

A warning about the look-alike: the everyday word gag (to choke or retch; to silence with a 'gag order'; a comedian's gag/joke) is NOT from this root. It is a separate, imitative word — the sound of someone gagging. It only happens to share spelling with the gage family, so don't try to link 'a gag joke' to 'a pledge.' They are unrelated.