Galileo and the church

What are Galileo's his most convincing arguments for saying that science and religion should not be regarded as antagonistic?

What role does mathematics play in Galileo's argument? How does he answer those who were concerned that a stationary sun and a moving earth were in conflict with the Bible, and with the story in Joshua (Book X: 12-14) where Joshua commands the sun to stop in the heavens over Gibeon in the battle with the Amorites in order to lengthen the day?

What does Galileo say is wrong with this argument? Why is this important to the point Galileo wishes to make about the Scriptures?

Was the "Letter" was an effective defense of Galileo's ideas or not?

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