This paper tries to show how in the theoretical justification of the study of naturally accelerated motion in the Discourses, Galileo would have combined three not perfectly identical methodological attitudes. Those attitudes would be: the ex-hypothesi demonstration from the astronomical tradition, realistically interpreted; the necessary demonstration from the Aristotelian and Euclidean tradition; the typical demonstration of the "mixed sciences". Thus, even Galileo's last work would be far from unequivocal as it regards scientific methodology.
Galileo; Discourses; naturally accelerated motion; ex hypothesi reasoning; Aristotle; Euclid; mixed sciences; optics