Paolo Bussotti

University of Udine | UNIUD · Department of Human Studies

Celebration of 200 years since Newton’s Philosophiae Naturalis Principia Mathematica Geneva Edition ([1739-1742]1822) Hosted by History of Physics and Applied Science & Technologies Team (HOPAST), IEMN, CNRS-University of Lille, France Institute of Electronics, Microelectronics and Nanotechnology Centre (IEMN), CNRS-University of Lille, France U...

In this research, an educational approach to the concept of energy is proposed. It is based on the history of physics. In 1854 Hermann Hemlholtz gave a popular lecture on the recent discovery that energy is conserved. Such lecture is used as a guide to introduce the pupils within several nuances of this concept. Not much mathematics is used, so Hel...

Among the mathematical methods which are taught in the last years of almost every high school, the mathematical induction deserves particular attention. It can be used both to define mathematical entities and to prove theorems. The second use is more common at high school level and is easier. Thus, I will basically focus on it, though analysing in...

DescartesDescartes, R.’ philosophy is one of the most studied and debated subject in the whole history of philosophy because of the innovative character of his metaphysics and theory of knowledge.

Before Newton, Johannes Kepler and Galileo GalileiGalilei, G. were the two most important scientists of the Modern Age and their contribution was essential in enabling Newton to achieve his final synthesis.

With regard to cosmology, Galileo was not an original thinker. He adhered to the Copernican system of the world and did not elaborate it further: he did not investigate the details of the form of the planetary orbits, he remained faithful to the traditional idea of their circular form and always rejected Kepler’s theory of elliptical orbits.

In the early modern ages, precise quantitative studies in astronomy concerned only the solar system (or the terrestrial system, if one refers to geocentric astronomy), and those bodies, like comets, which move—at least in some parts of their trajectories—in the proximity of the solar system.

In the context of an interdisciplinary approach aimed at pointing out the interconnections between science and philosophy in the early modern centuries, no author is probably more interesting than Leibniz.

In our interdisciplinary research concerning the relations between science and philosophy in the context of early modern cosmology, seven scientists are considered: Copernicus, Kepler, Galileo, Descartes, Huygens, Newton and Leibniz.

From a historical perspective, it is worth focusing on the context in which CopernicusCopernicus, N. lived and worked as well as on his scientific points of reference.

Newton is perhaps the greatest scientist of all time. It is difficult to conceive how a single man was able to obtain the results he achieved: Newton invented the infinitesimal calculus (credit for which also goes to Leibniz); he gave fundamental contributions to algebra and to algebraic geometry; as for optics, he devised a corpuscular theory and...

The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated many studies along the history of Western thought. The aim of this paper is to present the reading of Parmenides’s work offered by Federigo Enriques. It is based on several original theses: (1) Parmenide...

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 ellipt...

This research deals with a possible use of history of mathematics in mathematics education. In particular, history can be a fundamental element for the introduction of the concept of integral through a problem-centred and intuitive approach. Therefore, what follows is dedicated to the teaching of mathematics in the last years of secondary schools,...

“Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon” (p. Newton 1846, p. 83). This is the famous first axiom or law of motion stated by Newton in his masterpiece The Mathematical principles of natural philosophy (ivi). Everywhere, in the courses o...

Pierre de Fermat (1601/7–1665) 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 (Fermat 1891–1922, II, pp. 431–436). He wrote of numerous applications of this pro...

An interdisciplinary approach to education is nowadays considered an important aspect to improve the critical skills of the learners so that they can guess how several aspects of the human knowledge are interconnected. A key aspect of interdisciplinary education is represented by the use of the history of a certain subject within the teaching of th...

In this paper, I propose the idea that the French mathematician Michel Chasles developed a foundational programme for geometry in the period 1827–1837. The basic concept behind the programme was to show that projective geometry is the foundation of the whole of geometry. In particular, the metric properties can be reduced to specific graphic proper...

The concept of form is one of the most intuitive within our experience. When we say that two objects of different dimensions have or do not have the same form there is not properly a reflexion behind this claim. Rather, it is, at all appearances, based on our visual faculties, which is perfectly in order in the context of our daily life. This intui...

Michel Blay , Critique de l'histoire des sciences. Paris: CNRS Editions, 2017. Pp. 302. ISBN 978-2-271-09184-0. €22.00 (paperback). - Volume 51 Issue 1 - Paolo Bussotti

In this chapter, we present the concept of force in Kepler. We follow the development of this concept during Kepler’s scientific career, starting from his early considerations in the Mysterium Cosmographicum (1596) until his ripest conceptions expounded in the Epitome Astronomiae Copernicanae (1618–1621). Kepler tried to supply a dynamical explanat...

The purpose of this study is to illustrate Descartes' doctrine of circular motion, highlighting its foundations and difficulties. The connection of circular motion with other basic assumptions of Cartesian physics, in particular with the plentitude principle, is discussed. The mechanics behind the circular motion is examined, with reference to the...

The literature concerning the various methods by means of which the teaching of mathematics can be developed is simply huge and is increasing more and more. Several aspects are dealt with: the use of new technologies, especially as far as new computer programs or web sources are concerned; new techniques to develop calculations; researches concerni...

Abstract: The Geneva edition ([1739-1742] 1822) of Newton’s Principia is a very treasure for the historians of physics and mathematics. For, the editors added a series of notes, which are longer than Newton’s text itself. The explanations contained in such notes are important to grasp the way in which the spread of Newton’s thought was realized in...

Mathematics has always been a difficult issue, especially in the African countries. Mozambique is not an exception. This country had been colonized by Portugal until 1975. When the independence was obtained, a socialist regime was adopted (1977). The learning of mathematics entered the struggle against colonial and imperialistic ideas. Its best all...

Gottfried Wilhelm von Leibniz (1646-1716) has a prominent worldwide place in the history of scientific thought, from mathematics, logic, physics to the astronomy and engineering. In 2016, both his birth and death have been commemorated. Given both the influence by Leibniz on Western sciences & philosophies and his polyhedricity scientific activitie...

Il volume pone al centro della propria analisi il significato della scoperta scientifica come un vero e proprio manufatto intellettuale, frutto della creatività (e degli errori) del singolo ricercatore, ma anche risultato complesso di dinamiche sociali in cui si intrecciano contrasti tra le personalità dei singoli, conflitti tra gruppi di ricerca e...

Galileo Special Issue : Homage to Galileo Galilei 1564-2014. Reading Iuvenilia Galilean Works within History and Historical Epistemology of Science. Edited by Raffaele Pisano & Paolo Bussotti. Content Gerhard Heinzmann Editorial; Homage to Galileo Galilei 1564-2014 Raffaele Pisano & Paolo Bussotti Introduction. 1564-2014. Homage to Galileo Gali...

Based on our research regarding the relationship between physics and mathematics in HPS, and recently on Geneva Edition of Newton's Philosophiae Naturalis Principia Mathematica (1739–42) by Thomas Le Seur (1703–70) and François Jacquier (1711–88), in this paper we present some aspects of such Edition: a combination of editorial features and scienti...

In this paper we present the relations between mathematics and mathematics education in Italy between the 12th and the 16th century. Since the subject is extremely wide, we will focus on two case-studies to point out some relevant aspects of this phenomenon: 1) Fibonacci’s studies (12th-13th century); 2) Abacus schools. More particularly, Fibonacci...

I teach history of science at the University of Udine, Italy. My students – about 25 – frequently the second and the third year at the faculty of Letters and Philosophy (now called “Polo Umanistico”). They have to pass a sole proof in history of science. Therefore, in this editorial, I would like to face the problems connected with the teaching of...

In this paper, we present a brief history of the development of mechanics and mechanical machines theory (particularly in Lazare Carnot) and consequently the birth and advanced studies in thermodynamics and heat machines (particularly in Sadi Carnot) that influenced science & technology (as technoscience) in Western society between the eighteenth a...

What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significan...

During his stay in Padua ca. 1592–1610, Galileo Galilei (1564–1642) was a lecturer of mathematics at the University of Padua and a tutor to private students of military architecture and fortifications. He carried out these activities at the Academia degli Artisti. At the same time, and in relation to his teaching activities, he began to study the e...

This paper is the second part of our recent paper ‘Historical and Epistemological Reflections on the Culture of Machines around the Renaissance: How Science and Technique Work’ (Pisano & Bussotti 2014a). In the first paper—which discussed some aspects of the relations between science and technology from Antiquity to the Renaissance—we highlighted t...

The purpose of this paper is to valuate the role of geometry inside Enriques’ theory of knowledge and epistemology. Our thesis is that such a role is prominent. We offer a particular interpretation of Enriques’ gnoseology, according to which geometry is the cornerstone to fully catch also the way in which he framed his conception of the history of...

Kepler was one of the most important sources of inspiration for Leibniz. The influence of Kepler can be detected in numerous features of Leibniz’s planetary theory as well as in other aspects of his thought:

Leibniz explained the final version of his theory in the Illustratio Tentaminis de Motuum Coelestium Causis (1706). This work, which was not published in Leibniz’s lifetime, is divided into two parts. However, with regard to the content, it is possible to identify three conceptual cores:

This chapter is divided into four parts according to an ideal division of the Tentamen. In the first part Leibniz dealt with harmonic circulation and introduced paracentric motion; in the second one he analysed the properties of paracentric motion; in the third one he dealt with the inverse square law and the elliptic movements of the planets; in t...

In the general context of physics and in the planetary theory, in our specific case, the tendency of a rotating body to recede along the tangent is a fundamental element. We have seen that paracentric motion depends on the two opposite tendencies due to the solicitation of gravity and to the conate to recede. In terms of Newtonian physics the latte...

Leibniz’s planetary theory can be analysed without dealing with his conception concerning the origin of gravity and the causes of the planetary motions. It is possible to assume gravity and such causes as given since their origin and nature do not enter directly into the structure of Leibniz’s planetary theory. This perspective has been—in a sense—...

The aim of this book has been to point out the connections between Leibniz’s planetary theory and some of his general conceptions concerning physics and metaphysics as well as to identify the reasons why Leibniz felt the need to develop a planetary theory. We can summarize as follows:

Leibniz dealt with planetary theory in three papers written between 1689 and 1706. The first paper, titled Tentamen de Motuum Coelestium Causis, is the only one which was published—in the Acta Eruditorum Lipsiensium, 1689—during Leibniz’s lifetime. In the Tentamen Leibniz tried to construct a planetary theory based on a refinement and specification...

This book presents new insights into Leibniz’s research on planetary theory and his system of pre-established harmony. Although some aspects of this theory have been explored in the literature, others are less well known. In particular, the book offers new contributions on the connection between the planetary theory and the theory of gravitation. I...

In ancient Greece, the term “mechanics” was used when referring to machines and devices in general and intended to mean the study of simple machines (winch, lever, pulley, wedge, screw and inclined plane) with reference to motive powers and displacements of bodies. Historically, works considering these arguments were referred to as Mechanics (from...

This paper is divided into two parts, this being the first one. The second is entitled ‘Historical and Epistemological Reflections on the Culture of Machines around Renaissance: Machines, Machineries and Perpetual Motion’ and will be published in Acta Baltica Historiae et Philosophiae Scientiarum in 2015. Based on our recent studies, we provide he...

In some previous contributions of mine written for Scientia Educologica’s journals (Bussotti 2012; Bussotti, 2013; Bussotti, 2014) I dealt with the possible use of history of mathematics and science inside mathematics and science education. There is an abundant literature on this subject and I only tried to offer some ideas on possible educative it...

In the period 2012-2013 I got the qualification (abilitazione) to teach history and philosophy in the Italian high schools. The course I followed was called TFA (Tirocinio Formativo Attivo, Active Formative Training). The final examination was constituted by various proofs. Two of them were the written presentations of one educational itinerary in...

Mathematics education is also a social phenomenon because it is influenced both by the needs of the labour market and by the basic knowledge of mathematics necessary for every person to be able to face some operations indispensable in the social and economic daily life. Therefore the way in which mathematics education is framed changes according to...

My research fields are history of mathematics and science, mainly physics and astronomy. I have also published some works on mathematics and physics education (as to these works see Bussotti 2012a; Bussotti 2012b; Pisano-Bussotti, 2012; Bussotti 2013). I have often wondered which role history of science can have inside science education, basically...

In this paper we present some historical and epistemological notes to trace a general picture of the concept of force in Kepler with the aim to provide: a) conceptual bases of Keplerian notion of force; b) a stimulus to the Kepler Forschung as to this concept.

Generally speaking the exponential function has large applications and it is used by many non physicians and non mathematicians, too. Nevertheless some crucial and practical problems happen for its mathematical understanding. Mostly, this part of mathematical cognitive programmes introduce it from the mathematical strictly point of view. On the con...

This history of mathematics is a specific and, at the same time, wide field of research with proper methods, journals, congresses and results. However, some questions about its status are without any doubt legitimate. In particular: is the public to whom the work and the publications of the historians of mathematics are addressed, limited to the sp...

Georg Cantor, the founder of set theory, cared much about a philosophical foundation for his theory of infinite numbers. To that end, he studied intensively the works of Baruch de Spinoza. In the paper, we survey the influence of Spinozean thoughts onto Cantor’s; we discuss Spinoza’s philosophy of infinity, as it is contained in his Ethics; and we...

Optimal control theory is applied as a method for determining the minimum wind strength required for dynamic soaring of seabirds. Dynamic soaring is a flight technique by which seabirds extract energy from shear wind existing in an altitude layer close to the water surface. Mathematical models for describing the soaring motion of a bird and for the...

The genesis of the Lagrange multipliers is analyzed in this work. Particularly, the author shows that this mathematical approach was introduced by Lagrange in the framework of statics in order to determine the general equations of equilibrium for problems with constraints. Indeed, the multipliers allowed Lagrange to treat the questions of maxima an...