Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this (...) time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion. (shrink)

The most perplexing aspect of Galileo's work in physics is without doubt the sharp distinction one can draw between his essentially dynamic studies in such juvenilia as De Motu and the consciously kinematical approach of his later output—particularly the Two New Sciences. Whether one chooses to call this a shift from the “why” of motion to the “how”, or, as I should prefer, a shift from dynamics to kinematics, there can be no denying its existence. The Galileo who wrote that (...) “The present does not seem to be the proper time to investigate the cause of the acceleration of natural motion …” is, on the face of it, a very different man from the one who had earlier written almost an entire treatise on precisely this topic. (shrink)

The most reliable source for a reconstruction of Galileo's progress toward a science of motion is the series of undated fragmentary notes on that subject preserved in Codex A of the Galilean manuscripts at Florence. A gathering of such fragments was published by Favaro in the National Edition of Galileo's works, following the Discorsi. The more sophisticated fragments are clearly associated with the composition of that work, and show a definite and consistent understanding of acceleration. Eliminating those, it will be (...) found that the earlier notes fall into recognizable groups. First, there are some that refer to “moment of gravity”, or to the impetus of a body along a line of descent, and are associated with the discussion of inclined planes in De motu. Second, some refer to descent along arcs and chords of circles, associated with Galileo's letter of 29 November 1602 to Guido Ubaldo. These first two groups of notes do not explicitly refer to accelerated motion, and should not be assumed to do so implicity, where such an assumption can be avoided. (shrink)