Hamlet as a Dionysian man

According to Friedrich Nietzsche, Hamelet resembles the Dionysian man. Both gain knowledge, but refuse to take action, "for their action could not change anything in the eternal nature of things." (Nietzsche, 39) On the contrary, the Apolonian man would "take arms against a sea of troubles, and by opposing them end them." (Hamlet, 3:1:67-68) I do not agree with Nietsche that Hamlet represents the Dionysian man. When Hamlet is told the truth about his father's death, that it was his uncle who killed him and now is marrying his mother, he turns against his uncle. This shows how he, as the Apolonian man, strives to "set right a world that is out of joint." (Nietsche, 39) Here, in a desperate seek for revenge, Hamlet finds a motive for his actions. Even though Hamlet realizes that "action could not change anything in the eternal nature of things", meaning his father's death was something irreversible, he believes it is his destiny, the reason he was born. Therefore, I disagree with Nietsche's position that Hamlet is a Dionysian man.