The first thing that came to my mind when reading the expert from Dialogue Concerning The Two Chief Systems of the World- Ptolemaic & Copernican were the similarities in structure between it and Euthyphro. Not only is the structure of both pieces almost identical, the overall tones also mimic each other.
For the structure, Euthyphro and Simplicio are characterized in very similar matters. Both are supposed experts in their respective fields, and yet their ideas are easily refuted by their "challenger." Obviously, Salviati is Aristotle's parallel. Both take very sarcastic tones with their opponent and openly poke fun at their ignorance. Both men are also very planned in the attacks they make. They lull their opponents into a false sense of security about their own ideas, and then quickly bring them down with their logical reasoning. It appears that both characters intend to embarrass their opponents, simply to accentuate their view's validity. Dialogue is also broken up into four days, each presenting a different argument. This mimics the four arguments Euthyphro presents, all of which Aristotle refutes.
The overall tone of both pieces is similar as well. In both texts, the man refuting the ideas held by the "expert" (and society) takes a very sarcastic and at times openly hostile attitude. It is obvious that both Aristotle and Salviati lack respect for their opponents. Both believe their opponent's theories are bogus and they cannot understand how any person could belief such things. Neither man ever directly states these opinions, but through the tones they use it is obvious to the readers that both men feel this way.
While reading this excerpt, it was obvious how influential Aristotelian reasoning was on Galileo. His entire piece is modeled after it. Galileo lived during the Renaissance, a time when ancient texts were being rediscovered and held in high regard. Therefore, it only seems practical that Galileo would model his argument after one of the greatest, in his opinion, philosophers.