The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton’s perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics, but also the problematic aspects of his perfect geometrical (...) methods, more elegant, but less malleable than analytical procedures, of which Newton himself was one of the inventors. Furthermore, we will also consider the way in which Newtonianism was spread before in England and afterwards on continental Europe. In this respect the Geneva Edition plays a fundamental role because of its complete apparatus of notes, and because it appeared only thirteen years after the publication of the third edition of the Principia (1726). Finally, we will also confront some problems connected to the metaphysics of calculus. Therefore, the case of Newton is one of those in which, starting from mathematics applied to physics, it is possible to connect an impressive series of fundamental arguments such as the role of mathematics in science; the comparison between Newton’s geometrical methods and analytical methods; the way in which Newtonianism was spread as well as the philosophical implications of Newton’s mathematical concepts. (shrink)

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching (NoS) this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics (e.g., his arguments on electric–magnetic engine, mechanical equivalent of heat and free expansion) are dealt with. (shrink)

James Prescott Joule’s (1818–1889) bicentenary took place in 2018 and commemorated by the IDTC with a Symposium—‘James Joule’s Bicentenary: Scientific and Pedagogical Issues Concerning Energy Conservation’—at the European Society for the History of Science (ESHS & BSHS), 14th–17th September, 2018, in London. This symposium had three main objectives: It aimed specifically to celebrate James Joule’s achievements considering the most recent historiographical works with a particular focus on the principle of conservation of energy; It served the purpose of discussing the scientific (...) and pedagogical issues related to heat, energy and work and how they are presented in textbooks and worked out in classrooms; It also provided discussions on the present situation of teaching and learning science through the use of History of Science, both in K-12 and college level with an emphasis on energy and related concepts. In the following, the Introduction of this Special Issue on Joule is presented. (shrink)

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics are dealt with. (shrink)

Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the sum (...) of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

Review of The “Jesuit Edition” of Isaac Newton’s Principia.

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis (...) viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws. I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris. (shrink)

‘‘What Is Algebra?-Why This Book?’’ This is the amazing prelude to Taming the Unknown by Victor J. Katz, emeritus professor of mathematics at the University of the District of Columbia and Karen Hunger Parshall, professor of history of mathematics at the University of Virginia. This is an excellent book; its accurate historical and pedagogical purpose offers an accessible read for historians and mathematicians. [continue...].