I'm writing a paper about Aristotle's writing methods, so what is an examples for Patho, Etho, and Logos?

Examples of ethos can be shown in your speech or writing by sounding fair and demonstrating your expertise or pedigree:

"As a doctor, I am qualified to tell you that this course of treatment will likely generate the best results."

"My three decades of experience in public service, my tireless commitment to the people of this community, and my willingness to reach across the aisle and cooperate with the opposition, make me the ideal candidate for your mayor."

Logos

Using logos as an appeal means reasoning with your audience, providing them with facts and statistics, or making historical and literal analogies:

"The data is perfectly clear: this investment has consistently turned a profit year-over-year, even in spite of market declines in other areas."

"Ladies and gentlemen of the jury: we have not only the fingerprints, the lack of an alibi, a clear motive, and an expressed desire to commit the robbery… We also have video of the suspect breaking in. The case could not be more open and shut."

Pathos

Examples of pathos can be seen in language that draws out feelings such as pity or anger in an audience:

"If we don't move soon, we're all going to die! Can't you see how dangerous it would be to stay?"

"I'm not just invested in this community - I love every building, every business, every hard-working member of this town."

Explanation:

which is the following what are you asking?

so is this a rhetorical question?