It is generally agreed that Galileo’s distinctive place in the history of science is due to the power of his method, and that, in general terms, this consists in an effective combination of mathematics and physical experiment. In attempting to be more specific, some authors have assigned a particular method to Galileo as either new or a unique adaptation of a traditional method, e.g. hypothetico-deduction, the method of analysis, or ex suppositione. William Wallace, for example, has argued that by the (...) time of the «Two New Sciences» (1638) Galileo had fashioned his own version of ex suppositione, combining elements of the Archimedean and Aristotelian traditions into a distinct two-stage mode of reasoning of his own creation. We shall have reason to comment upon this below. (shrink)