The English Galileo

Shining a light on Harriot and Galileo: On the mechanics of reflection and projectile motion

“…Harriot's research into a theory of projections can be traced from around the 1580s to at least 1606, and culminated in his 'inclined plane conception of projectile motion'. 24 Harriot resolved that a cannonball's ballistic motion into two component motions: (a) a motion along the line of sight/shot, decelerating due to air resistance, which he conceived as being analogous to a ball rolling up an inclined plane (see Figure 2), such that this slowing motion depended upon the law of the inclined plane, i.e. the sine of the angle of inclination (elevation); and (b) an accelerating vertical motion of freefall.…”

“…26 Secondly, he added that the times of these two vertical motions are 'equal to the time of vertical fall from the highest point of the trajectory to the ground'. 27 These statements have been interpreted by Schemmel as proposing 'the identity of a projectile's motion in the vertical direction with the motion of vertical projection', and thus the vertical component motion (under the action of gravity) would be independent of the horizontal component motion. He points out that the conceptual source of such statements is historically uncertain, that 'it is plausible to assume that they had their origin in theoretical considerations', and suggests that considerations of the simplest case of projectile motion -vertical projection and fall -may have led Harriot to these kinematical principles.…”

“…The mathematical method and its application can be briefly explicated via Figures 3 and 4 (below). Given the point q reached by a heavy body in upward oblique projection in a certain time (Figure 3), 30 Harriot calculated the distance b which would have been covered in freefall in this time, then projected it onto the line of sight/shot giving the length a, and by drawing down the vertical distance b again from this point on the line he thereby obtained the construction point p of the parabola. 31 Applying this process at several points along the line of sight/shot provided sufficient construction points p for Harriot to trace out the curve of the parabolic trajectory.…”

Giordano Bruno and Bonaventura Cavalieri's theories of indivisibles: a case of shared knowledge

“…For without a comparison of Galileo and Harriot "our understanding of the shared knowledge of early modern thinking […] will remain incomplete and biased". 5 Mutatis mutandis, we can apply what Schemmel says about Galileo and Harriot to the case of Bruno and Cavalieri. A comparison between these two authors, besides enriching the image we have of Bruno as a mathematician, might also clarify the historical conditions under which the rise of geometrical indivisibles occurred. In my view, it can help to identify an important component of early modern mathematical culturethat is, the Pythagorean tradition from which both Bruno and Cavalieri gained the insight that geometrical objects are generated by motion.…”

“…As noted by Schemmel, independence is a key factor for historical epistemology to be effective, otherwise the search for shared knowledge boils down to a "trivial matter". 7 Such an independence in not guaranteed in the case of seventeenth-century "indivisibilists" who explicitly refer to Cavalieri as the father of their methods.…”