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.