18 found
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  1.  10
    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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  2.  27
    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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  3.  30
    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.  27
    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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  6.  12
    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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  7.  8
    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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  8.  35
    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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  9. Aritmetica e aritmetizzazione: la via indicata da Gauss e Kronecker.Paolo Bussotti - 2000 - Epistemologia 23 (1):23-50.
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  10. Il problema dei fondamenti della matematica all'inizio dell'Ottocento.Paolo Bussotti - 2000 - Theoria 2000:83-95.
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  11. Il problema dei fondamenti della matematica negli scritti giovanili di Bernard Bolzano.Paolo Bussotti - 1998 - Epistemologia 21 (2):225-244.
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  12. Introduction. 1564-2014. Homage to Galileo Galilei.Raffaele Pisano & Paolo Bussotti - 2017 - Philosophia Scientae 21:7-15.
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  13.  8
    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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  14.  11
    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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  15.  18
    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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  16.  8
    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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  17.  4
    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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  18. 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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