The Scientific Revolution spawned not just one methodology, but two. We have emphasized Bacon's inductivism at the expense of Galileo's more abstract, sophisticated method of successive approximation, and so have failed to appreciate Galileo's contribution to the ceteris paribus problem in philosophy of science. My purpose here is to help redress this imbalance. I first briefly review the old unsolved problems, and then point out the Baconian basis of ceteris paribus, as this clause is conventionally understood, and its history from (...) Aristotle to twentieth century Positivism. Then I explore Galileo's method of dealing with unwanted impediments, and the more general problem of 'accidents.' I trace his methodology back to Archimedes and forward through the economic theories of Adam Smith (18th century), J. S. Mill (19th) and Milton Friedman (20th). Finally, I point out ways in which I think Galileo's scientific method sheds light on, and provides a partial solution to, the ceteris paribus problem. (shrink)