In Act I, Scene II, Prospero is speaking to Miranda and telling her how they came to be on the island. He describes his brother Antonio’s treachery. Prospero enjoyed studying and concentrated on that more than on governing Milan. He left the governing of Milan to Antonio, his brother. Antonio immediately began scheming with Naples to take the Dukedom from his brother. “My brother and thy uncle, called Antonio—I pray, mark me!—that a brother should be so perfidious!” Eventually, Antonio moves in, and with help from an army sent by Naples, he takes the Dukedom and sends Prospero and Miranda off to die on the ocean. "This King of Naples, being an enemy to me inveterate, hearkens my brother’s suit…a treacherous army levied one midnight…"
In Act II, we meet Antonio and Sebastian, the brother of the King of Naples. Antonio, who has stolen his brother’s dukedom, is now encouraging Sebastian to seize his brother’s throne by murdering him. Sebastian is a little reluctant, at first, but then he remembers that Antonio took his brother’s dukedom: “I remember you did supplant your brother Prospero.” After Antonio reassures him that he will be glad when his brother is dead, he encourages Antonio to kill the king, telling him he will no longer owe taxes to Naples. “Draw thy sword. One stroke shall free thee from the tribute which thou payest.”
The comparison is simple. In the first act, Prospero is talking about the treachery of his brother and his enemy. In the second act, two of the people who conspired against him are contemplating the most treacherous act of all: killing a king.