I like to think that “The Gift of the Magi” uses all three of ethos, pathos and logos in order to convince the reader of the themes that we should be careful how we make choices and love is more important than money. First of all, by bringing in the concept of the Magi and the gifts they gave the baby Jesus, O’ Henry draws on ethos (associating famous or credible people with your idea) by using the credibility of the Magi to convince readers of his message.
Pathos is the use of emotion to sell an idea. We really feel sorry for the young couple, and so it makes us think about how we make choices and what is really important to us.
Logos is the use of logic to sell an idea. In this case, we can clearly see a logical result between wasteful presents and the pain the young people caused one another, and their happiness when they realize they still have each other.