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Italian word grazie comes from Latin ago, Proto-Indo-European *gʷr̥H-
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, [...]
*gʷr̥H- (Proto-Indo-European)
gratias agere (Latin)
grazia (Italian)
(chiefly, in the plural) serif. (legal) pardon. Favour, kindness. Grace.
grazie (Italian)
(uncommon) gratitude. Thanks, thank-you (an expression of gratitude) Thank you, thanks!.