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Latin word purgatorius comes from Latin ago, Latin purus (Clean; pure. Clear, limpid.)
ago (Latin)
(of offerings) I slay, kill (as a sacrifice). (of plants) I put forth, sprout, extend. (of time) I pass, spend. I accomplish, manage, achieve. I chase, pursue. I discuss, plead, deliberate. I do, act, make, behave. I drive at, pursue (a course of action). I drive, conduct. I guide, govern, administer. I perform, transact. I push, move, impel. I rob, steal, plunder, carry off. I stir up, [...]
purus (Latin)
Clean; pure. Clear, limpid.
purgare (Latin)
purgatorius (Latin)
Cleansing, purgative, purgatory.