Homage to Evangelista Torricelli's Opera Geometrica 1644-2024 : Text, Transcription, Commentaries and Selected Essays As New Historical Insights

• Autore: Pisano Raffaele
• Pubblicazione: Cham : , : Springer International Publishing AG, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (1118 pages)
• Altri autori: DhombresJean Radelet de GravePatricia BussottiPaolo
• Nota di contenuto: Intro -- Remarks for the Reader -- About the Authors and Contributors -- Torricelli Research Project Leader -- Torricelli Project Scientific Committee -- Torricelli Project Scientific Editorial Staff -- Authors' Book and Essays -- Invited Contributor's Essays -- Financial Support Torricelli--History of Physics Project -- Contents -- Opera Geometrica, 1644 -- 1 Celebrating Evangelista Torricelli's Opera Geometrica (1644-2024): Details in History and Historiography of Physics, Geometry and Mathematics -- Abstract -- 1 Torricelli's Life and Works -- 1.1 Adventures and Misadventures -- 2 Presenting Torricelli's Opera Geometrica -- 2.1 The Content of Opera Geometrica -- 2.2 A Historiography of Torricelli's Opera Geometrica and Works -- 2.3 Torricelli In Quibus Archimedis Doctrina -- 3 A Selection from Torricelli's Opera Geometrica Proofs -- 3.1 De Sphaera Et Solidis Sphaeralibus -- 3.2 De Motu Gravium Naturaliter Descendentium -- 3.3 The Quadrature of the Parabola and the Cubature of the Acute Hyperbolic Solid -- 4 Intermezzo 1645-1646: The Works on the Infinite Curves -- 4.1 De Infinitis Spiralibus (1645) -- 4.2 De Infinitis Hyperbolis (Ca. 1646) -- 5 Infinitesimal Calculus and Indivisibles -- 6 Concluding Remarks -- Acknowledgments -- References -- Selected Essays -- 2 Introducing Selected Essays on Opera Geometrica (1644) -- Abstract -- 1 Selected Essays -- Acknowledgements -- References -- 3 Encounters with Infinity: From Torricelli to Gödel -- Abstract -- 1 Torricelli's Shocker -- 2 Leibniz Exploits the Infinite -- 3 Euler Factors a Polynomial of Infinite Degree -- 4 Cantor Leaves Us a Conundrum -- 5 Infinitesimals Achieve Legitimacy -- 6 Conclusion: Gödel's Legacy -- References -- 4 A New Cycloid Narrative Centered on Torricelli and Roberval to Understand the Diverse Ways of the Mathematical Revolution -- Abstract. ; 1 Introduction. The Honesty of a Scientist and Its Relevance for Historians of Science -- 1.1 The Ignorant Despises What He Cannot Reach -- 1.2 Why then to Scrutinize Such Historical Texts? -- 1.3 Oblivion in History of Mathematics -- 2 A Story Told in Terms of Problem Solving -- 2.1 The "Helena of Geometers" -- 2.2 Mersenne Took Care of Letters, Playing the Role of Intermediary Between the Geometers of Each of the Two Nations -- 2.3 The Bad Guy is Named: The Other Story About the "Plagiarist" Jean de Beaugrand -- 3 When the Story Involves Methods -- 3.1 It Is Possible That Torricelli and Roberval Have Found the Measure of an Arch, Each in His Way? -- 3.2 Today All Philosophers Agree That Nothing Is Known of Things Apart from the Various Relations Which They Have Between Themselves -- 3.3 The Verse Sine Function, or the Curve in Orthogonal Axes -- 3.4 What We Learn About Functions from the Step with Calculus? -- 3.5 "Candid" Silences in Narratives on Two Different Representations of the Cycloid -- 4 Mathematics Alone? -- 4.1 The Childhood of Geometry -- 4.2 A Unity of Material as Torricelli Said, or Progress in All Domains as Mersenne Perceived? -- 4.3 Rolling and Sliding: Mersenne's Way of Eliminating Paradoxes on Infinity, on Divisibility and on the Continuous -- 4.4 The Narrative from Drawings: Classical Versus Baroque Frame of Reference for the Cycloid -- 5 About Discoveries -- 5.1 What About the Uses of Such a Curve? -- 5.2 Representations and Frames of Reference -- 5.3 Composition of Movements and Robervalian Triangles -- 5.4 Another Narrative with Serendipity, or the Contrast Between Good Fortune, Recognition of an Invention and Long Search -- 6 Conclusion -- 7 Bibliography -- Annexes -- Annex 1. Translation of a Letter Sent by Torricelli to Roberval, October 1st, 1643. ; Annex 2. Translation of the Appendix on the Measure of the Cycloid in Torricelli's Opera Geometrica (1644) -- Annex 3. An English Translation of the Original Two Pages from Mersenne About the Roulette in Harmonie Universelle, 2nd Vol. -- Annex 4. Partial Translation of the Tractatus duo of John Wallis, Published in 1659 and Concerning the Torricelli-Roberval Quarrel -- Annex 5. Speech by Jacob Bernoulli on the History of the Cycloid -- References -- 5 Historical and Methodological Details on the De Motu Gravium Naturaliter Descendentium in Torricelli's Opera Gometrica (1644) -- Abstract -- 1 An Outline -- 1.1 The Structure of This Paper -- 2 An Introduction to Torricelli's Principle and Its Physical-Epistemological Status -- 2.1 The Structure of De Motu Gravium Naturaliter Descendentium -- 2.2 The Praemittamus Within Torricelli's Frameworks -- The Praemittamus and Its Context -- Analysis of the Praemittamus -- A Historical and Terminological Annotation -- 2.3 Archimedes's Influence on Torricelli -- 2.4 On Galilean Aggregatum and Torricellian Simul Coniuncta -- 2.5 Another Method of Application of Torricelli's Principle -- 3 The Praemittamus and the Principle of Virtual Work -- 4 The Methodological Status of Torricelli's Principle -- 4.1 The Physics of the Principles and Forces. Conceptual Developments -- 4.2 An Interplay Between Galileo and Torricelli upon Physics and Mathematics Relationship -- 5 Concluding Remarks -- Acknowledgements -- References -- 6 Torricelli's Proof of Galileo's Assumption on the Velocity Acquired at the End of a Free Fall -- Abstract -- 1 Introduction -- 2 Galileo's Assumption and Torricelli's Reaction to It -- 2.1 Torricelli's Praemittimus -- 3 Galileo's So Called "Confusion" Between Archimedean Momentum and His New Momentum in Proofs Concerning the Inclined Plane. ; 3.1 De motu antiquiora (1589-1592). The Apparent Weight on an Inclined Plane -- 3.2 Le mecaniche (1593), the Momentum to Go Down -- 3.3 Viviani's Addition (1639) to the Discorsi: De motu naturaliter accelerato -- 4 Torricelli's Proof of Galileo's Assumption -- 4.1 Torricelli's Principle -- 4.2 Torricelli's Proposition I -- 4.3 Torricelli's Proposition II -- 4.4 Torricelli's Lemma to Proposition II -- 4.5 Torricelli's Corollarium to Proposition II -- 4.6 Torricelli's Scholium to Proposition II -- 4.7 Torricelli's Proposition III: Proof of His Praemittimus Key to the Proof of Galileo's Assumption -- 4.8 Torricelli's corollarium to Proposition III -- 4.9 Torricelli's Lemma to Proposition III -- 4.10 Torricelli's Second Part of the Proof of Galileo's Theorem of Chords -- 4.11 Torricelli's Proposition IV -- 4.12 Torricelli's Second Proof of Proposition IV -- 4.13 Torricelli's Proposition V -- 5 Galileo's Proof of His Supposition -- 5.1 In Galileo's Manuscript in Possession of Viviani, Written After the Publication of the Discorsi -- 5.2 In Viviani's Addition to the Discorsi -- 6 Conclusion -- 6.1 On Galilean Momentum -- 6.2 On the Notion of Function -- References -- 7 Why Publish a Book of Geometry in Seventeenth-Century Europe? Science, Status, and Print Culture in Evangelista Torricelli's Opera Geometrica (1644) -- Abstract -- 1 Introduction -- 2 Mathematics and Book Publication in the 17th Century: The Anomalous Case of Galileo -- 3 Mathematics and Book Publication in the 17th Century-Other Models -- 4 Torricelli and the Publication of the Opera Geometrica -- 5 Conclusion. Reading the Opera Geometrica in Light of Its Print Agendas -- References -- Critical Transcription of the Opera Geometrica, 1644 -- 8 Opera Geometrica (1644) Transcription: General Considerations -- Acknowledgements -- 9 Opera Geometrica (1644) Transcription: Image-Text Side by Side. ; Abstract -- Acknowledgements -- Bibliography: Evangelista Torricelli, Main Sources -- Abstract -- Bibliography -- Author Index -- Subject Index.
• Titolo autorizzato: Homage to Evangelista Torricelli's Opera Geometrica 1644-2024
• ISBN: 3-031-06963-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910845480103321
• Lo trovi qui: Univ. Federico II
• Serie: Logic, Epistemology, and the Unity of Science Series