Answer:
In the provided excerpt from John F. Kennedy's "Rice Stadium Moon Speech," the most prevalent rhetorical appeal is Logos.
Logos is an appeal to logic and reason. In this excerpt, Kennedy presents a logical argument by outlining the rapid technological advancements and progress that humanity has made over a relatively short span of time, emphasizing how far and how fast humanity has come in terms of scientific and technological achievements. He uses a chronological sequence of historical events to support his argument, appealing to the audience's sense of reason and the logical progression of human history to justify the space exploration efforts and investments he is discussing.