ag

The root ag is the present-stem form of the same Latin verb that gives us act: agere, "to do, drive, lead, set in motion." Where act- (from the past participle actus) leans toward the thing done, ag- keeps the verb in motion — it's the driving itself.

The clearest survivors are easy to feel:

- agent = ag- + -ent (one who) → "the one who does/drives." An agent is the active party — the doer behind the deed, whether a secret agent, a real-estate agent, or a chemical agent that makes a reaction happen.
- agenda is pure Latin grammar fossilized: it's the plural of agendum, "a thing that must be done." Your agenda is literally your list of things-to-be-done.
- agile = ag- + -ile → "easy to drive / quick to move." An agile body or mind is one that can be set in motion fast.
- agitate = agit- (frequentative of agere, "to keep driving") + -ate → to drive again and again: shake a liquid, stir up a crowd, or churn the mind into anxiety.

From here ag drives off into less obvious territory through prefixes, because agere shifts its vowel to -ig- or -eg- inside compounds:

- ex- (out) + agere → exigere gives exigent (pressing, driving you to act now) and exiguous (driven down to scanty leftovers)
- co- (together) + agere → cogere ("drive together, compel") gives cogent (an argument that drives you together to one conclusion) and coagulate (drive particles together into a clot)
- prod- (forth) + agere → prodigere ("drive forth, squander") gives prodigal (one who drives money out the door)

Greek had a cousin verb, agein, also "to lead/drive," which sneaks in through borrowed words: strategy (stratos army + agein lead = the general's art of leading), pedagogy (pais child + agein lead = leading children, i.e. teaching), and agony (agōn, a contest one is driven into — the struggle).

The through-line: wherever you see ag/ig/eg and sense driving, leading, or setting in motion, you're looking at agere. Its twin act- is the same verb after the action is finished.