Reasoning with the Infinite: From the Closed World to the Mathematical UniverseUniversity of Chicago Press, 1998 - 216 pagina's Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis. "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion."—Margaret Wertheim, New Scientist |
Inhoudsopgave
Introduction | 1 |
Infinity Eliminated or Huygenss Theory of the Motion of Heavy Bodies | 13 |
2 Mathematical Speculations about Curvilinear Falls | 18 |
3 The Deductive Scheme of the Science of the Motion of Heavy Bodies | 27 |
First and Last Ratios in the Newtonian Theory of Central Forces | 38 |
Centrifugal Force and Weight | 43 |
3 The Deductive Scheme of Newtons Principia | 52 |
The Science of Motion in the Workshops of Infinity | 70 |
Motion Algorithmized | 108 |
2 The New Algorithmic Science of Motion | 118 |
Fontenelle and the Reasons of Infinity | 131 |
1 The Mathematics of Infinity | 133 |
2 Mathematical Physics and the Rationalization of Infinites | 145 |
Notes | 165 |
| 193 | |
| 211 | |
Overige edities - Alles bekijken
Reasoning with the Infinite: From the Closed World to the Mathematical Universe Michel Blay Geen voorbeeld beschikbaar - 1998 |
Veelvoorkomende woorden en zinsdelen
accelerated motion acquired analysis central forces centripetal force Christiaan Huygens conatus conceive continuous curve cycloid definition degrees of speed degrees of velocity demonstration Descartes differential calculus Discorsi edition Edme Mariotte equal Euclidean express falling bodies finite follows Fontenelle Fontenelle's formulas Galileo geometric géométrie George Berkeley given Gottfried Wilhelm Leibniz heavy bodies Histoire Hobbes Huygens's Ibid indivisibles infinitesimal infinitesimal Calculus infinity instant Jean Bernoulli Joseph-Louis Lagrange l'infini Lagrange Leibniz Leibnizian calculus magnitude mathematical physics matter mécanique method Michel Blay motu mouvement moveable nature Newton ordinates paper parallel Paris passage Philosophy Pierre Varignon plane Principia principle problems proportional proposition ratio reason Registres relation rest result Royal Academy Royale des Sciences science of motion space traversed square tangents theorem things Thomas Hobbes tion Torricelli trajectories trans triangle uniform motion uniformly accelerated versed sine weight Wronski
Populaire passages
Pagina 198 - Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences. Plus la Dioptrique, les Météores et la Géométrie, qui sont des essais de cette méthode.
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