This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo’s characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat’s proof. The second part illustrates how a physical and a mathematical insight enabled Fermat’s result, and that a simple modification would satisfy any of Fermat’s critics. The result is an illustration of how a purely theoretical argument can settle an apparently empirical debate.

ArgumentThis paper discusses the theory of motion of the philosopher Honoré Fabri (1608–1688), a senior representative of early modern Jesuit scientists. It argues that the consensus prevailing among historians – according to which Fabri's theory of impetus is diametrically opposed to Galileo's or Descartes' concept of inertia – is false. It shows: that Fabri carefully constructed his concept of impetus in order to easily incorporate the principle of linear conservation of motion (designated here as “limited inertia”), by adopting formal (rather (...) than efficient) causality between impetus and motion and by allowing impetus to act only along straight lines; that he explicitly deemed Aristotle's famous “inertial paradox” not as a paradox at all; and that linear conservation of motion was not limited to “counterfactual” circumstances but played a significant part in his discrete theory of free fall and constituted an integral component of his general physical (and even mathematical) philosophy. However, the paper also shows that Fabri's notion of inertia was restricted to one dimension only, and therefore should indeed be considered “limited.” In his analysis of horizontal projectiles, Fabri explicitly rejected Galileo's important principle of superposition, and thus revealed significant constraints to his “inertial” thinking. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

This research presents in a different way the new science of motion described in Galileo’s Discourses (1638) and in Evangelista Torricelli’s Geometrical Work (1644). We will focus on how the local motion has been mathematized at the beginning of the modern mechanics in order to analyse its conditions and main features. The local motion, which had been a topic of natural philosophy, became a topic of modern kinematics that is a science. We will show that the new structure of speed (...) has been a crucial event that led the naive notion of speed of the ancient tradition to the technical notion of continuous magnitude. The nature of continuity is closely connected to infinity and an analysis of this link is the peculiar way of reading those two texts. (shrink)