Galileo is arguing, in the dialogue concerning "Two New Sciences",
against the Aristotelian assertion that things fall "in proportion to
their weight" -- meaning the one twice as heavy will fall twice as fast.
I am not sure that Galileo's argument is so specious. He says in essence
that one can view a 3 kg object as a 2kg and a 1 kg in contact with each
other. If Aristotle were correct, then the 1 kg object would be -- on
its own -- falling at half the speed of the 2 kg, and would thus tend to
slow down the 2 kg when the two are in contact, producing a resulting
speed that is LESS than that of the 2 kg object alone, but the two
together are a 3 kg object and should produce a speed that is MORE than
the 2 kg object alone. The only way out of the contradiction is that the
objects fall at the same rate independent of the weight. I haven't done
this in some years, but I found students to be pretty interested in this
argument, especially when drawn out to answer the questions themselves
so that the contradiction is really apparent.
Jerry Epstein