Galileo vs. Aristotle on Free Falling Bodies

This essay attempts to demonstrate that it is doubtful if Galileo's famous thought experiment concerning falling bodies in his 'Dialogues Concerning Two New Sciences' (Galileo  1954: 61-64) actually does succeed in proving that Aristotle was wrong in claiming that "bodies of different weight […] move […] with different speeds which stand to one another in the same ratio as their weights," (Galileo  1954: 61). (Part I); and further that it is likewise doubtful that that argument does or even can establish Galileo's own famous 'Law of Falling Bodies,' viz., that regardless of their weight all bodies fall with the same speed. (Part II)