Raffaele Pisano

In this paper, we deal with Torricelli’s principle in mechanics according to which two heavy bodies linked together cannot move by themselves unless their common centre of gravity descends. At the beginning of the De motu gravium naturaliter descendentium, in his Opera geometrica (1644), Evangelista Torricelli (1608–1647) expressed this principle in a very brief section entitled Praemittamus. Our aim is to sustain the idea that Torricelli was constructing a general view of a kind of physics based on general principles, of which the previous one is the most important and explicit statement. In our discussion, the following themes are addressed: (1) a comparison between the Torricelli’s principle and the virtual work principle; (2) the role of Torricelli principle within the history of the virtual work principle; (3) the logic behind the demonstrations offered in physics relying on general principles such as that of Torricelli.

InCelebratingthisDIUMessayHistoriographywe describeIEMNTorricelli’s lifeLille Universityand worksUdine University in their scientific context, including the ArchimedeanArchimedean heritage in Torricelli’s works. We analyse the changes of Torricelli’s works and explain the novelties of the edition we are offering. Then, we provide a picture of the most significant results obtained by Torricelli (1608–1647), particularly in mechanicsMechanicsand geometryGeometry. Furthermore, we also focus on the Torricelli’s methodology, specifying how he provedProved two of his achievements, given their novelty and mathematical meaning: (a) the volumeVolume of the “solido acutissimo”; (b) the geometryGeometryof theLogarithmic Spirallogarithmic spiralGeometric Spiral. AnContent ad hoc ad hocAd hocContentContent of the Opera geometricaOpera geometrica is proposed as well. It is based on the original chronological sequences of the contentsContent wrote by Torricelli. This is important to evaluate the birth of the scientific matters presented by Torricelli and the editorial process of the publicationPublication.

Two topics, Science and History, have been studied for centuries, if not millennia, often in disjointed ways. The realization that Science is nourished by its History is quite obvious nowadays and is a standpoint shared by all the contributors in this book. Given this fact, the following chapters were written by interdisciplinary scholars who are experts in this field. The admirably written contributions concern History of Science, Epistemology, Philosophy of Science, but are not restricted to these disciplines. They also discuss theoretical perspectives and ingenious results achieved by beautiful and clever minds working together or inspired by one another. Torricelli’s history is a fascinating one, filled with struggles and insights that have been studied and examined in depth by internationally renowned specialists. The gripping stories reconstructed, as well as the epistemological and logical threads drawn from long and painstaking research, are presented in a clear and absorbing fashion, in each instance with a unique style and always with considerably talented analysis. The preceding celebratory historical and historiographical chapter on Opera geometrica (Torricelli in Opera geometrica. Florentiae. Masse & de Landis (1644); Torricelli in Opere di Evangelista Torricelli edite in occasione del III centenario della nascita col concorso del Comune di Faenza da Gino Loria e Giuseppe Vassura. Montanari (1919–1944)) is also a structured introductory essay to the contents of this extensive Springer research project. Below, the reader will find summaries of selected distinguished essays written in order to celebrate the magnificence of Torricelli’s Opera geometrica. The whole volume has to be considered as an homage both to Opera geometrica and to Evangelista, a genial scientist.

Evangelista Torricelli exemplifies the use the moderns made of the ancients' mathematical methods. Celebrating Evangelista Torricelli's monumental Opera geometrica, this book marks 380 years since its publication (1644-2024). This homage to Torricelli introduces the magnificent major work in Mechanics and Mathematics of a brilliant Archimedean–and–Galilean scientist to modern readers. Opera geometrica deals with Motion & Mechanics and Geometry & Infinitesimals. In quibus Archimedis doctrina Torricelli also presents his mechanical principle of equilibrium – the foundation of the modern Principle of Virtual Work/Static. This outstanding source and research book spotlights the relevance and originality of Torricelli’s Mechanics, and is the first and most profound analysis of the Opera geometrica to date. The historical study is achieved in extensive Introduction, 5 Essays and an accurate Transcription of Opera geometrica with parallel side–by–side text, including substantive explicative notes. The book is an accessible avenue to understanding this work by leading authorities who offer much-needed insights into the relationship Physics–Mathematics, Mechanics and Fundamentals. It appeals to historians, epistemologist and scientists.

The literature of the past century produced an historical reconstruction of statics theory applied to mechanical structures coinciding–starting with Le Mecaniche (1634) and Discorsi e dimostrazioni matematiche sopra a due nuove scienze (1638) by Galileo Galilei (1564–1642). Based on previous research (RP) and our historical and historiographical line of research [37], in this paper we briefly analyse Buonaiuto Lorini (1540–1611) Le Fortificationi ([1596] 1609) as a bridge between the science of weights and early mechanical science, including the graphical scale and machines. This is a fundamental and advanced military fortification–engineering treatise with an evident important relationship between theory & practice, including designs–projects of both fortresses and machines, understood as tools, to manufacture them. Lorini also presents an excursus on how fortifications developed according to the advent of new artillery/weapons, comprising the crucial passage from the use of square to circular towers up to the description of modern fortresses in all their details, e.g., bulwarks and cavaliers, curtains, orillons, star–shaped plans. Basing on Archimedes’ (fl. 287–212 BCE) techniques (law of the lever) and Guidobaldo del Monte's (1545–1607; Le Mecaniche (1577–1581) he successfully engaged in advanced mechanical considerations. His position (at the end of the first chapter) on the distinction between the mathematician (scientist) and the mechanician (architect–engineer or even machine expert) is historiographically very interesting within the difference between abstract Euclidean geometry and the application of its contents to imperfect and heterogeneous reality. The translations are ours.

This book presents a historical and scientific analysis as historical epistemology of the science of weights and mechanics in the sixteenth century, particularly as developed by Tartaglia in his Quesiti et inventioni diverse, Book VII and Book VIII (1546; 1554). In the early 16th century mechanics was concerned mainly with what is now called statics and was referred to as the Scientia de ponderibus, generally pursued by two very different approaches. The first was usually referred to as Aristotelian, where the equilibrium of bodies was set as a balance of opposite tendencies to motion. The second, usually referred to as Archimedean, identified statics with centrobarica, the theory of centres of gravity based on symmetry considerations. In between the two traditions the Italian scholar Niccolò Fontana, better known as Tartaglia (1500?-1557), wrote the treatise Quesiti et inventioni diverse (1546). This volume consists of three main parts. In the first, a historical excursus regarding Tartaglia's lifetime, his scientific production and the Scientia de ponderibus in the Arabic-Islamic culture, and from the Middle Ages to the Renaissance, is presented. Secondly, all the propositions of Books VII and VIII, by relating them with the Problemata mechanica by the Aristotelian school and Iordani opvsculvm de ponderositate by Jordanus de Nemore are examined within the history and historical epistemology of science. The last part is relative to the original texts and critical transcriptions into Italian and Latin and an English translation. This work gathers and re-evaluates the current thinking on this subject. It brings together contributions from two distinguished experts in the history and historical epistemology of science, within the fields of physics, mathematics and engineering. It also gives much-needed insight into the subject from historical and scientific points of view. The volume composition makes for absorbing reading for historians, epistemologists, philosophers and scientists.

Gottfried Wilhelm von Leibniz (1646-1716) has a prominent worldwide place in the history of scientific thought, from mathematics, logic, and physics to astronomy and engineering. In 2016, both his birth and death have been commemorated. Given the influence by Leibniz on Western sciences and philosophies and his polyhedric scientific activities, this special book chooses to focus on Leibniz's scientific works. In particular, we explore Leibniz's intellectual matrix and heritage within interdisciplinary fields, and present contributions from leading experts on the subject. The book offers much-needed insights into the subject from scientific, historical, philosophical and nature of science perspectives. It also provides authoritative introductions to scholarly contributions, which are often dispersed in journals and books not easily accessible to every reader. Therefore, this volume also contains excellent chapters on topics which, generally speaking, have their place in any rounded science, history or philosophy topic. It provides an absorbing and significant read for historians, philosophers and scientists alike. Editors Raffaele Pisano is full professor at the Lille University, France. Michel Fichant is Emeritus professor at the Sorbonne University, France. Paolo Bussotti is senior lecturer-researcher at the Udine University, Italy. Agamenon R. E. Oliveira is full professor at the Federal University of Rio de Janeiro, Brazil. Foreword Eberhard Knobloch is Emeritus professor at the Berlin University of Technology, Germany.

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.

We present historical and epistemological notes on the relationships between Chemistry–Physics as dating back to two scientific revolutions: Lavoisier’s Traité Élémentaire de Chimie (1789) and by Sadi Carnot’s Réflexions sur la Puissance Motrice du Feu (1824). Their scientific paradigms and mathematical interpretations of chemical and physical phenomena did not made use of infinitesimal analysis as, i.e., exposed within mechanics and, generally speaking, they were totally different from notable Newtonian paradigm survived until to 19th century. An anomaly was, and two revolutions were produced.

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.

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.

After the birth of thermodynamics’ second principle—outlined in Carnot's Réflexions sur la puissance motrice du feu —several studies provided new arguments in the field. Mainly, they concerned the thermodynamics’ first principle—including energy conceptualisation—, the analytical aspects of the heat propagation, the statistical aspects of the mechanical theory of heat. In other words, the second half of nineteenth century was marked by an intense interdisciplinary research activity between physics and chemistry: new disciplines applied to the heat developed in the form of analytical, mechanical and statistical theories. Inside all these theories, entropy—the brand-new function that Clausius coined in his Mechanical theory of heat—started to play a central epistemic role. In the present paper, we analyse some steps of the historical process of conceptualisation of such function from 1850 to 1902. Particularly, we retrace the historical–foundational path that—starting from Clausius’ Second Law—lead Boltzmann and Gibbs to their distinguished formulations of statistical entropy. As usual, our research has been unrolled through the analyses of primary sources and by leaning on critical readings of the secondary literature. As for the methodological approach, text analysis of historical documents constituted our privileged modus operandi. This paper is the expression of a collaborative historical research program focused on the thermodynamic foundations of physics–chemistry relationship; early results have already been published by the same authors upon the concepts of reversibility––and––thermal equilibrium.

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.

This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare Carnot – l'organisateur de la victoire – in Essai sur le machine en général (1786) assumed that the generalization of machines was a necessity for society and its economic development. Subsequently, his new coming science applied to machines attracted considerable interest for technician, as well, already in the 1780’s. With no lack in rigour, Carnot used geometric and trigonometric rather than algebraic arguments, and usually went on to explain in words what the formulae contained. His main physical– mathematical concepts were the Geometric motion and Moment of activity–concept of Work . In particular, he found the invariants of the transmission of motion (by stating the principle of the moment of the quantity of motion) and theorized the condition of the maximum efficiency of mechanical machines (i.e., principle of continuity in the transmission of power). While the core theme remains the theories and historical studies of the text, the book contains an extensive Introduction and an accurate critical English Translation – including the parallel text edition and substantive critical/explicative notes – of Essai sur les machines en général (1786). The authors offer much-needed insight into the relation between mechanics, mathematics and engineering from a conceptual, empirical and methodological, and universalis point of view. As a cutting–edge writing by leading authorities on the history of physics and mathematics, and epistemological aspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology).

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.

To commemorate the 50th anniversary of his passing, this special book features studies on Alexandre Koyré, one of the most influential historians of science of the 20th century, who re-evaluated prevalent thinking on the history and philosophy of science. In particular, it explores Koyré’s intellectual matrix and heritage within interdisciplinary fields of historical, epistemological and philosophical scientific thought. Koyré is rightly noted as both a versatile historian on the birth and development of modern science and for his interest in philosophical questions on the nature of scientific knowledge. In the 1940s and 1950s his activities in the United States established a crucial bridge between the European historical tradition of science studies and the American academic environments, and an entire generation of historians of science grew up under his direct influence. The book brings together contributions from leading experts in the field, and offers much-needed insights into the subject from historical, nature of science, and philosophical perspectives. It provides an absorbing and revealing read for historians, philosophers and scientists alike.

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.

Forums, I extensively analysed Tartaglia’s corpus: science of weights, geometry, arithmetic, mathematics and physics–trajectories of the projectiles, fortifications, included its intelligibility science in the military architecture. The latter is exposed in Book VI of the Quesiti et invention diverse. In Quesiti there is La Gionta del sesto libro—a kind of appendix to the Book VI containing drawings of the geometric shape of the Italian fortifications. It is based on Euclidean geometry and other figures where a scale is displayed. The interest—included intellectual history and cultural foundations of science—is: what is the role–played by La Gionta del sesto libro in the Quesiti? Is it independent booklet/speeches? If yes, when Tartaglia did write it? In this paper, I present an historical–philological–foundational hypothesis on the Tartaglia’s fortifications corpus, as exposed in the Book VI and La Gionta del sesto libro; with respect to dates of editions of Quesiti. This goal is important to make historically clear both the editorial role–played by Curzio Troiano Navò in the Tartaglia’s corpus before—after Tartaglia’s death and the particular interest and development of subject of fortifications by Tartaglia between 1537–1546 and 1554.

Forums, I extensively analysed Tartaglia’s corpus: science of weights, geometry, arithmetic, mathematics and physics–trajectories of the projectiles, fortifications, included its intelligibility science in the military architecture. The latter is exposed in Book VI of the Quesiti et invention diverse. In Quesiti there is La Gionta del sesto libro—a kind of appendix to the Book VI containing drawings of the geometric shape of the Italian fortifications. It is based on Euclidean geometry and other figures where a scale is displayed. The interest—included intellectual history and cultural foundations of science—is: what is the role–played by La Gionta del sesto libro in the Quesiti? Is it independent booklet/speeches? If yes, when Tartaglia did write it? In this paper, I present an historical–philological–foundational hypothesis on the Tartaglia’s fortifications corpus, as exposed in the Book VI and La Gionta del sesto libro; with respect to dates of editions of Quesiti. This goal is important to make historically clear both the editorial role–played by Curzio Troiano Navò in the Tartaglia’s corpus before—after Tartaglia’s death and the particular interest and development of subject of fortifications by Tartaglia between 1537–1546 and 1554.

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable intellectual wealth—are conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set.