How Galileo dropped the ball and Fermat picked it up (Q542147)

This paper tells an episode from the history of physics. There were two competing schools in the 17th century dealing with the freefall, a Galilean school and a Jesuit one. Fermat agreed that Galileo's conclusion remained undemonstrated but suggested that Galileo might have had a correct proof in mind. Fermat picked up the ball and gave a mathematical proof. Unfortunately, Fermat's proof made a connection that wasn't obvious. The second part of the reviewed paper shows that a simple modification would satisfy any of Fermat's critics.