The mathematical principles of natural philosophy: an annotated translation of the Principia
Newton's 'Principia' is perhaps the second most famous work of mathematics, after Euclid's 'Elements'. Originally published in 1687, it gave the first systematic account of the fundamental concepts of dynamics, as well as three beautiful derivations of Newton's law...
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| Zusammenfassung: | Newton's 'Principia' is perhaps the second most famous work of mathematics, after Euclid's 'Elements'. Originally published in 1687, it gave the first systematic account of the fundamental concepts of dynamics, as well as three beautiful derivations of Newton's law of gravitation from Kepler's laws of planetary motion. As a book of great insight and ingenuity, it has raised our understanding of the power of mathematics more than any other work. This heavily annotated translation of the third and final edition (1726) of the 'Principia' will enable any reader with a good understanding of elementary mathematics to grasp easily the meaning of the text, either from the translation itself or from the notes, and to appreciate some of its significance. All forward references are given to illuminate the structure and unity of the whole, and to clarify the parts. The mathematical prerequisites for understanding Newton's arguments are given in a brief appendix |
| Beschreibung: | Literaturverzeichnis: Seite [728]-734 |
| Beschreibung: | xlv, 743 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107020658 |
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| 520 | 3 | |a Newton's 'Principia' is perhaps the second most famous work of mathematics, after Euclid's 'Elements'. Originally published in 1687, it gave the first systematic account of the fundamental concepts of dynamics, as well as three beautiful derivations of Newton's law of gravitation from Kepler's laws of planetary motion. As a book of great insight and ingenuity, it has raised our understanding of the power of mathematics more than any other work. This heavily annotated translation of the third and final edition (1726) of the 'Principia' will enable any reader with a good understanding of elementary mathematics to grasp easily the meaning of the text, either from the translation itself or from the notes, and to appreciate some of its significance. All forward references are given to illuminate the structure and unity of the whole, and to clarify the parts. The mathematical prerequisites for understanding Newton's arguments are given in a brief appendix | |
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| adam_text | Contents Frontispiece page ii Translator’s Preface Halley’s Ode The Author’s Preface to the Reader ix xxv xxviii The Author’s Preface to the Second Edition xxxi The Editor’s Preface to the Second Edition xxxii The Author’s Preface to the Third Edition xlvi Definitions 1 The Axioms, or The Laws of Motion 15 On the Motion of Bodies, Book One 31 §1.1. On the theory of limits, which is used to deduce later results 33 §1.2. On the calculation of centripetal forces 47 §1.3. On the motion of particles in eccentric conic sections 69 §1.4. On the calculation of elliptical, parabolic, and hyperbolic orbits 84 §1.5. On the calculation of orbits when neither focus is given 93 §1.6. On the calculation of motion in given orbits 122 §1.7. On the ascent and descent of particles in a straight line 135
VI Contents §1.8. On the calculation of the orbits in which particles revolve under any centripetal forces 146 §1.9. On the motion of particles in moving orbits, and the motion of the apsides 156 §1.10. On the motion of particles on given surfaces, and the swing ing motion of a string pendulum 168 §1.11. On the motion of particles attracting each other by centripetal forces 183 §1.12. On the attractive forces of spherical bodies 216 §1.13. On the attractive forces of non-spherical bodies 235 §1.14. On the motion of particles attracted by centripetal forces towards the various parts of arbitrarily large bodies 247 On the Motion of Bodies, Book Two 255 §11.1. On the motion of particles moving against a resistance that is proportional to the speed 257 §11.2. On the motion of bodies moving against a resistance that is proportional to the square of the speed 269 §11.3. On the motion of bodies to which the resistance consists of one part that is proportional to the speed, and another to the square of the speed 297 §11.4. On the circular motion of bodies in resisting media 309 §11.5. On the density and compression of fluids, and on hydrostatics 318 §11.6. On the motion and resistance of string pendulums 331 §11.7. On the motion of fluids and the resistance of projectiles 363 §11.8. On motion propagated through fluids 406 §11.9. On the circular motion of fluids 425
vii Contents On Celestial Mechanics, Book Three 443 Introduction to Book Three 445 The Rules of Scientific Argument 447 Phenomena 450 Propositions 456 On the Motion of the Nodes of the Moon 535 General Scholium 632 Appendix A: Mathematical Notation and Results assumed in The Principia 639 Appendix B: Calculus in The Principia 653 Appendix C: Newton’s Astronomy 666 Appendix D: Newton’s Theory of Tides 670 Appendix E: Technical Terms used in the Translation 672 Appendix F: On Newton’s Style, and Translating The Principia 683 Appendix G: Some Difficult Words 698 Appendix H: Astrological Symbols 706 Appendix I: Glossary of Latin Terms 707 Appendix J: Technological Illustrations 725 References 728 Index 735
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Contents Frontispiece page ii Translator’s Preface Halley’s Ode The Author’s Preface to the Reader ix xxv xxviii The Author’s Preface to the Second Edition xxxi The Editor’s Preface to the Second Edition xxxii The Author’s Preface to the Third Edition xlvi Definitions 1 The Axioms, or The Laws of Motion 15 On the Motion of Bodies, Book One 31 §1.1. On the theory of limits, which is used to deduce later results 33 §1.2. On the calculation of centripetal forces 47 §1.3. On the motion of particles in eccentric conic sections 69 §1.4. On the calculation of elliptical, parabolic, and hyperbolic orbits 84 §1.5. On the calculation of orbits when neither focus is given 93 §1.6. On the calculation of motion in given orbits 122 §1.7. On the ascent and descent of particles in a straight line 135
VI Contents §1.8. On the calculation of the orbits in which particles revolve under any centripetal forces 146 §1.9. On the motion of particles in moving orbits, and the motion of the apsides 156 §1.10. On the motion of particles on given surfaces, and the swing ing motion of a string pendulum 168 §1.11. On the motion of particles attracting each other by centripetal forces 183 §1.12. On the attractive forces of spherical bodies 216 §1.13. On the attractive forces of non-spherical bodies 235 §1.14. On the motion of particles attracted by centripetal forces towards the various parts of arbitrarily large bodies 247 On the Motion of Bodies, Book Two 255 §11.1. On the motion of particles moving against a resistance that is proportional to the speed 257 §11.2. On the motion of bodies moving against a resistance that is proportional to the square of the speed 269 §11.3. On the motion of bodies to which the resistance consists of one part that is proportional to the speed, and another to the square of the speed 297 §11.4. On the circular motion of bodies in resisting media 309 §11.5. On the density and compression of fluids, and on hydrostatics 318 §11.6. On the motion and resistance of string pendulums 331 §11.7. On the motion of fluids and the resistance of projectiles 363 §11.8. On motion propagated through fluids 406 §11.9. On the circular motion of fluids 425
vii Contents On Celestial Mechanics, Book Three 443 Introduction to Book Three 445 The Rules of Scientific Argument 447 Phenomena 450 Propositions 456 On the Motion of the Nodes of the Moon 535 General Scholium 632 Appendix A: Mathematical Notation and Results assumed in The Principia 639 Appendix B: Calculus in The Principia 653 Appendix C: Newton’s Astronomy 666 Appendix D: Newton’s Theory of Tides 670 Appendix E: Technical Terms used in the Translation 672 Appendix F: On Newton’s Style, and Translating The Principia 683 Appendix G: Some Difficult Words 698 Appendix H: Astrological Symbols 706 Appendix I: Glossary of Latin Terms 707 Appendix J: Technological Illustrations 725 References 728 Index 735 |
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| spelling | Newton, Isaac 1643-1727 Verfasser (DE-588)118587544 aut (DE-588)4232118-9 Philosophiae naturalis principia mathematica The mathematical principles of natural philosophy an annotated translation of the Principia Isaac Newton ; translated and annotated by C.R. Leedham-Green Cambridge Cambridge University Press 2021 xlv, 743 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite [728]-734 Newton's 'Principia' is perhaps the second most famous work of mathematics, after Euclid's 'Elements'. Originally published in 1687, it gave the first systematic account of the fundamental concepts of dynamics, as well as three beautiful derivations of Newton's law of gravitation from Kepler's laws of planetary motion. As a book of great insight and ingenuity, it has raised our understanding of the power of mathematics more than any other work. This heavily annotated translation of the third and final edition (1726) of the 'Principia' will enable any reader with a good understanding of elementary mathematics to grasp easily the meaning of the text, either from the translation itself or from the notes, and to appreciate some of its significance. All forward references are given to illuminate the structure and unity of the whole, and to clarify the parts. The mathematical prerequisites for understanding Newton's arguments are given in a brief appendix Newton, Isaac 1643-1727 Philosophiae naturalis principia mathematica (DE-588)4232118-9 gnd rswk-swf Geschichte 1726 gnd rswk-swf Naturphilosophie (DE-588)4041408-5 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Newton, Isaac / 1642-1727 / Principia Mechanics / Early works to 1800 Principia (Newton, Isaac) Mechanics Early works (DE-588)4135952-5 Quelle gnd-content Newton, Isaac 1643-1727 Philosophiae naturalis principia mathematica (DE-588)4232118-9 u DE-604 Mechanik (DE-588)4038168-7 s Physik (DE-588)4045956-1 s Mathematik (DE-588)4037944-9 s Naturphilosophie (DE-588)4041408-5 s Geschichte 1726 z Leedham-Green, Charles Richard 1940- (DE-588)115706046 edt trl Erscheint auch als Online-Ausgabe 978-1-139-10580-4 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032107062&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Newton, Isaac 1643-1727 The mathematical principles of natural philosophy an annotated translation of the Principia Newton, Isaac 1643-1727 Philosophiae naturalis principia mathematica (DE-588)4232118-9 gnd Naturphilosophie (DE-588)4041408-5 gnd Physik (DE-588)4045956-1 gnd Mechanik (DE-588)4038168-7 gnd Mathematik (DE-588)4037944-9 gnd |
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| title | The mathematical principles of natural philosophy an annotated translation of the Principia |
| title_GND | (DE-588)4232118-9 |
| title_alt | Philosophiae naturalis principia mathematica |
| title_auth | The mathematical principles of natural philosophy an annotated translation of the Principia |
| title_exact_search | The mathematical principles of natural philosophy an annotated translation of the Principia |
| title_exact_search_txtP | The mathematical principles of natural philosophy an annotated translation of the Principia |
| title_full | The mathematical principles of natural philosophy an annotated translation of the Principia Isaac Newton ; translated and annotated by C.R. Leedham-Green |
| title_fullStr | The mathematical principles of natural philosophy an annotated translation of the Principia Isaac Newton ; translated and annotated by C.R. Leedham-Green |
| title_full_unstemmed | The mathematical principles of natural philosophy an annotated translation of the Principia Isaac Newton ; translated and annotated by C.R. Leedham-Green |
| title_short | The mathematical principles of natural philosophy |
| title_sort | the mathematical principles of natural philosophy an annotated translation of the principia |
| title_sub | an annotated translation of the Principia |
| topic | Newton, Isaac 1643-1727 Philosophiae naturalis principia mathematica (DE-588)4232118-9 gnd Naturphilosophie (DE-588)4041408-5 gnd Physik (DE-588)4045956-1 gnd Mechanik (DE-588)4038168-7 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Newton, Isaac 1643-1727 Philosophiae naturalis principia mathematica Naturphilosophie Physik Mechanik Mathematik Quelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032107062&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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