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Paolo Bussotti [27]P. Bussotti [1]
  1.  40
    A Newtonian tale details on notes and proofs in Geneva edition of Newton's Principia.Raffaele Pisano & Paolo Bussotti - 2016 - BSHM-Journal of the British Society for the History of Mathematics:1-19.
    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 scientific aims. The proof of Proposition XLIII is presented and commented as a case study.
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  2.  25
    Historical and Foundational Details on the Method of Infinite Descent: Every Prime Number of the Form 4 n + 1 is the Sum of Two Squares.Paolo Bussotti & Raffaele Pisano - 2020 - Foundations of Science 25 (3):671-702.
    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 (...)
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  3.  43
    Newton’s Philosophiae Naturalis Principia Mathematica "Jesuit" Edition: The Tenor of a Huge Work.Raffaele Pisano & Paolo Bussotti - 2014 - Rendiconti Accademia Dei Lincei Matematica E Applicazioni 25 (4):413-444.
    This paper has the aim to provide a general view of the so called Jesuit Edition (hereafter JE) of Newton’s Philosophiae Naturalis Principia Mathematica (1739–1742). This edition was conceived to explain all Newton’s methods through an apparatus of notes and commentaries. Every Newton’s proposition is annotated. Because of this, the text – in four volumes – is one of the most important documents to understand Newton’s way of reasoning. This edition is well known, but systematic works on it are still (...)
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  4. On the Jesuit Edition of Newton’s Principia. Science and Advanced Researches in the Western Civilization.Raffaele Pisano & Paolo Bussotti - 2014 - Advances in Historical Studies 3 (1):33-55.
    In this research, we present the most important characteristics of the so called and so much explored Jesuit Edition of Newton’s Philosophi? Naturalis Principia Mathematica edited by Thomas Le Seur and Fran?ois Jacquier in the 1739-1742. The edition, densely annotated by the commentators (the notes and the comments are longer than Newton’s text itself) is a very treasure concerning Newton’s ideas and his heritage, e.g., Newton’s geometry and mathematical physics. Conspicuous pieces of information as to history of physics, history of (...)
     
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  5.  32
    Fibonacci and the Abacus Schools in Italy. Mathematical Conceptual Streams - Education and its Changing Relationship with Society.Raffaele Pisano & Paolo Bussotti - 2015 - Almagest 6 (2):126-164.
    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, probably the greatest European mathematician of the Middle Ages, made the calculations with Hindu-Arabic digits widely spread in Europe; Abacus schools were also based on the teaching of (...)
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  6.  31
    Historical and Epistemological Reflections on the Culture of Machines around the Renaissance: How Science and Technique Work?Raffaele Pisano & Paolo Bussotti - 2014 - Acta Baltica Historiae Et Philosophiae Scientiarum 2 (2):20-42.
    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 here a historical and epistemological feature on the role played by machines and machineries. Ours is an epistemological thesis based on a series of historical examples to show that (...)
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  7.  46
    Galileo in Padua: architecture, fortifications, mathematics and “practical” science.Raffaele Pisano & Paolo Bussotti - 2015 - Lettera Matematica Pristem International 2 (4):209-222.
    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 equilibrium of bodies and strength of materials, later better structured and completed in his Dialogues Concerning Two New Sciences of 1638. This paper examines (...)
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  8.  27
    Historical and Epistemological Reflections on the Culture of Machines around the Renaissance: Machines, Machineries and Perpetual Motion.Raffaele Pisano & Paolo Bussotti - 2015 - Acta Baltica Historiae Et Philosophiae Scientiarum 3 (1):69-87.
    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’. In the first paper—which discussed some aspects of the relations between science and technology from Antiquity to the Renaissance—we highlighted the differences between the Aristotelian/Euclidean tradition and the Archimedean tradition. We also pointed out the way in which the two traditions were perceived around the Renaissance. The Archimedean tradition is connected with machines: its (...)
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  9.  23
    Michel Chasles’ foundational programme for geometry until the publication of his Aperçu historique.Paolo Bussotti - 2019 - Archive for History of Exact Sciences 73 (3):261-308.
    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 properties. In the attempt to prove the validity of his conception, Chasles made fundamental contributions to the theory of polarity and also understood that a satisfactory development (...)
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  10.  18
    The dialogue between sciences, philosophy and engineering: new historical and epistemological insights: homage to Gottfried W. Leibniz 1646-1716.Raffaele Pisano, Michel Fichant, Paolo Bussotti, Agamenon R. E. Oliveira & Eberhard Knobloch (eds.) - 2017 - London: College Publications.
    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. (...)
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  11.  14
    Introducing Selected Essays on Opera Geometrica (1644).Raffaele Pisano & Paolo Bussotti - 2023 - In Raffaele Pisano, Jean Dhombres, Patricia Radelet de Grave & Paolo Bussotti (eds.), Homage to Evangelista Torricelli’s Opera Geometrica 1644–2024: Text, Transcription, Commentaries and Selected Essays as New Historical Insights. Springer Verlag. pp. 95-97.
    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 (...)
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  12.  11
    The Geometrical Foundation of Federigo Enriques’ Gnoseology and Epistemology.Paolo Bussotti & Raffaele Pisano - unknown
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  13.  44
    Parmenides, the Founder of Abstract Geometry: Enriques Interpreter of the Eleatic Thought.Paolo Bussotti - 2023 - Foundations of Science 28 (3):947-975.
    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) Parmenides was the discoverer of abstract geometry; (2) his critics was addressed against the Pythagoreans rather than against Heraclitus; (3) Parmenides discovered and applied the contradiction and the (...)
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  14.  7
    Opera Geometrica (1644) Transcription: Image–Text Side by Side.Raffaele Pisano, Paolo Bussotti & Patricia Radelet de Grave - 2023 - In Raffaele Pisano, Jean Dhombres, Patricia Radelet de Grave & Paolo Bussotti (eds.), Homage to Evangelista Torricelli’s Opera Geometrica 1644–2024: Text, Transcription, Commentaries and Selected Essays as New Historical Insights. Springer Verlag. pp. 283-1088.
    This section provides the first full edited transcription—from Latin and Italian vernacular language—of the Opera geometrica. Further, as above said, facsimile texts are added, including our critical comments as footnotes to this chapter.
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  15.  6
    Historical and Methodological Details on the De Motu Gravium Naturaliter Descendentium in Torricelli’s Opera Gometrica (1644).Raffaele Pisano & Paolo Bussotti - 2023 - In Raffaele Pisano, Jean Dhombres, Patricia Radelet de Grave & Paolo Bussotti (eds.), Homage to Evangelista Torricelli’s Opera Geometrica 1644–2024: Text, Transcription, Commentaries and Selected Essays as New Historical Insights. Springer Verlag. pp. 189-224.
    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 (...)
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  16.  31
    Conceptual Frameworks on the Relationship Between Physics–Mathematics in the Newton Principia Geneva Edition (1822).Raffaele Pisano & Paolo Bussotti - 2022 - Foundations of Science 27 (3).
    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 (...)
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  17.  15
    Alcuni aspetti del pensiero di Federigo Enriques e la nascita del Centro Enriques.Paolo Bussotti - 2002 - Rivista di Storia Della Filosofia 4.
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  18. Aritmetica e aritmetizzazione: la via indicata da Gauss e Kronecker.Paolo Bussotti - 2000 - Epistemologia 23 (1):23-50.
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  19. Il problema dei fondamenti della matematica all'inizio dell'Ottocento.Paolo Bussotti - 2000 - Theoria 2000:83-95.
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  20. Il problema dei fondamenti della matematica negli scritti giovanili di Bernard Bolzano.Paolo Bussotti - 1998 - Epistemologia 21 (2):225-244.
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  21.  19
    Michel Blay, Critique de l'histoire des sciences. Paris: CNRS Editions, 2017. Pp. 302. ISBN 978-2-271-09184-0. €22.00.Paolo Bussotti - 2018 - British Journal for the History of Science 51 (1):153-155.
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  22.  19
    Quantità, gradazione e intensità nelle opere fisiche di Descartes.Paolo Bussotti - 2016 - In Thomas Leinkauf & Thomas Kisser (eds.), Intensität Und Realität: Systematische Analysen Zur Problemgeschichte von Gradualität, Intensität Und Quantitativer Differenz in Ontologie Und Metaphysik. De Gruyter. pp. 103-128.
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  23. Some aspects of the thought of Federigo Enriques and the foundation of the Centro-Enriques.P. Bussotti - 2002 - Rivista di Storia Della Filosofia 57 (4):621-630.
     
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  24.  54
    The influence of Spinoza’s concept of infinity on Cantor’s set theory.Paolo Bussotti & Christian Tapp - 2009 - Studies in History and Philosophy of Science Part A 40 (1):25-35.
    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 attempt to draw a parallel between Spinoza’s and Cantor’s ontologies. Our conclusion is that the study of Spinoza provides deepening insights into Cantor’s (...)
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  25.  10
    Introduction. 1564-2014. Homage to Galileo Galilei.Raffaele Pisano & Paolo Bussotti - 2017 - Philosophia Scientiae 21:7-15.
    1 The Iuvenilia–Early Galilean works When Galileo Galilei (1564-1642) published the Sidereus Nuncius in 1610 [Galilei 1890-1909, III, pt 1, 51-96], he was a famous enough scientist, who was not young: for, he was 46. Nevertheless, this little book represented the fundamental turning point in Galileo’s life and scientific production. The Sidereus Nuncius was very successful and gave rise to numerous discussions. Some scholars defended Galileo—the most important was Kepler—, many others, with a...
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  26.  30
    Machines, Machineries and Perpetual Motion: Historical and Epistemological Reflections on the Culture of Machines around the Renaissance.Raffaele Pisano & Paolo Bussotti - 2015 - Acta Baltica Historiae Et Philosophiae s Cientiarum 3 (1):69-87.
    This paper is the second part of our recent paper ‘Historical and Epistemological Reflections on the Culture of machines around the renaissance: How s cience and t echnique 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 the differences between the Aristotelian/Euclidean tradition and the Archimedean tradition. We also pointed out the way in which the two traditions were perceived around the r enaissance. t (...)
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  27.  7
    Celebrating Evangelista Torricelli’s Opera Geometrica (1644–2024): Details in History and Historiography of Physics, Geometry and Mathematics. [REVIEW]Raffaele Pisano & Paolo Bussotti - 2023 - In Raffaele Pisano, Jean Dhombres, Patricia Radelet de Grave & Paolo Bussotti (eds.), Homage to Evangelista Torricelli’s Opera Geometrica 1644–2024: Text, Transcription, Commentaries and Selected Essays as New Historical Insights. Springer Verlag. pp. 3-92.
    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”; (...)
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  28.  18
    Homage to Evangelista Torricelli’s Opera Geometrica 1644–2024: Text, Transcription, Commentaries and Selected Essays as New Historical Insights.Raffaele Pisano, Jean Dhombres, Patricia Radelet de Grave & Paolo Bussotti (eds.) - 2023 - Springer Verlag.
    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 (...)
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