Title: From the epicycles of the Greeks to Kepler's ellipse - The breakdown of the circle paradigm

Abstract: The principle that celestial bodies must move on circular orbits or on paths resulting from the composition of circular orbits has been assumed as a constant guide in the astronomical thougth of the peoples facing the Mediterranean sea as from the second century B.C. until the beginning of the XVII century. The mathematical model based on such an assumption, the theory of epicycles in all its versions and modifications, has been taken as a scheme for all astronomical calculations during at least eighteen centuries, from Hipparcus to Kepler. As it is known, in Astronomia Nova (1609), Kepler succeded to establish the two laws which after him were named the first and the second Kepler's laws. The revolution he performed by giving up the circle paradigm is of fundamental importance and represents the indispensable premise to Newtonian theory. This revolution, the result of what Kepler called his "war" against Mars, is usually underestimated if one considers the break carried out with respect to the pre-Kepler celestial kinematics. In "Astronomia Nova" we assist to the attempt of Kepler to get for Mars an orbit consistent with the results of Tycho Brahe's observations. Passing through several phases and step by step discarding the hypoteses wich gave results in contrast with observations, Kepler arrived at establishing that the orbit of Mars around the Sun is an ellipse. Here an esposition is given of this work of analysis by Kepler wich is, in the history of science, one of the early examples of rigorous setting up of a model which correctly explains the experimental results.