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The Geometrization of Motion: Galileo’s Triangle of Speed and its Various Transformations

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This article analyzes Galileo’s mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law of fall. The article also shows how Galileo’s discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day Three of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo’s law of free fall, replaced Galileo’s diagrams of acceleration with alternative ones.


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1. Interdisciplinary Science Reviews, 03080188 2004; Vol 29: 259
2. british journal for the history of science. 00070874 1969; Vol 4: 340
3. Physis, 01037331 1974; Vol 16: 309
4. Archive for History of Exact Sciences, 00039519 1974; Vol 13: 103
5. Early Science and Medicine 13837427 1999; Vol 4: 269

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