Final answer:
The answer that is not one of the appeals listed by the textbook figure for use in argument essays is analogy, as it does not represent one of the primary rhetorical appeals of ethos, pathos, and logos.
Step-by-step explanation:
The textbook illustrates that there are three primary rhetorical appeals used by writers in an argument essay: ethos (ethical appeal), pathos (emotional appeal), and logos (logical appeal). These appeals work to persuade audiences in different ways. Ethos focuses on establishing credibility or ethical standing, pathos seeks to connect with the audience's emotions, and logos is based on logical reasoning and evidence. From the information provided, it is evident that analogy, while a strategy used for clarification in writing, is not directly listed as one of the three main types of rhetorical appeals in the context of argument essays.