Final answer:
Thomas Paine uses pathos as the most prominent kind of rhetorical appeal in this excerpt from Common Sense.
Step-by-step explanation:
The most prominent kind of rhetorical appeal that Thomas Paine uses in this excerpt from Common Sense is pathos. Pathos is an appeal to emotion, and Paine evokes emotions such as frustration and urgency to convey his message. By using phrases like 'for God's sake' and 'cutting throats', Paine appeals to the reader's emotions, creating a sense of urgency and the need for immediate action.