Newton's Principia revisited


Book Description

PROBLEM. The treatise is devoted to the reconstruction of our 'instinctive beliefs' in classical mechanics and to present them 'as much isolated and as free from irrelevant additions as possible'. The same motivation has driven many authors since the publication of Newton's Principia. IMPORTANCE. Classical mechanics will remain the basic reference and tool for mechanics on terrestrial and planetary scale as well as the proto-theory of relativistic and quantum mechanics. But it can only serve its purpose if it is not considered as obsolete, but if its foundations and implications are understood and made 'absolutely' clear. METHOD. Based on the 'instinctive belief' that the foundations of classical mechanics cannot be found and reconstructed within mechanics itself but only 'outside', classical mechanics is 'understood' by embedding it into an adequate theory of knowledge and adequate proto- and meta-theories in terms of the 'language of dynamics'. Evidence is produced that available philosophical expositions are not adequate for the purpose at hand. Mechanics is treated as part of physics, not of mathematics. Not sophisticated mathematical artifacts, necessary for solving specific problems, but the intellectually satisfactory foundation of mechanics in general is subject and purpose of the exercise. The goal is reached using axiomatic systems as models. SCOPE. Following an account of the unsatisfactory state of affairs the treatise covers the epistemological foundations, abstract proto-mechanics, i. e. the theories of time and space, meta-mechanics, i. e. the theories of state space models and of quantities proper, and, as an instance of the latter, abstract elementary mechanics, the theory of translational motions of 'small' solid bodies in three-dimensional Euclidean space, including classical general relativity. Subsequently the theory of classical kinematics is developed as basis for interpreted proto-mechanics and interpreted elementary mechanics. As an amus







Oxford Handbook of Newton


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Rethinking the Scientific Revolution


Book Description

This book challenges the traditional historiography of the Scientific Revolution, probably the single most important unifying concept in the history of science. Usually referring to the period from Copernicus to Newton (roughly 1500 to 1700), the Scientific Revolution is considered to be the central episode in the history of science, the historical moment at which that unique way of looking at the world that we call 'modern science' and its attendant institutions emerged. It has been taken as the terminus a quo of all that followed. Starting with a dialogue between Betty Jo Teeter Dobbs and Richard S. Westfall, whose understanding of the Scientific Revolution differed in important ways, the papers in this volume reconsider canonical figures, their areas of study, and the formation of disciplinary boundaries during this seminal period of European intellectual history.




Edmond Halley


Book Description

Edmond Halley (1656-1742), MA, LLD, FRS, Capt. RN, Savillian Professor of Geometry and Astronomer Royal, stands pre-eminent among Oxford, English, and European scientists. A contemporary of Wren, Pepys, Hooke, Handel, Purcell, and Dryden, he was a schoolboy in London while the Great Fireraged, and was an active participant in the Enlightenment, an age of profound developments in all the arts and sciences. As a younger contemporary of Isaac Newton, he had a crucial part in the Newtonian revolution in the natural sciences. It was Halley who set the question that led Newton to writethe Principia, and who edited, paid for, and reviewed it. In later years he applied the methods of the Principia widely in astronomy and geophysics. Now more widely known for his prediction of the return of "his" comet, Halley discovered the proper motion of stars, made important studies of themoon's motion, and his investigations of the Earth's magnetic field and of tides were unrialled for centuries. His prediction of the transit of Venus led to Cook's voyage to Tahiti. He was far more than an cloistered academic; his exploits as a naval captain led to perilous adventures, and he wasalso a notable servant of the State. Much material about his eventful career has come to light in recent years, making this a timely new account of the life, scientific interests, and continuing influence of this engaging and adventurous scholar. Sir Alan Cook has written a fascinating andilluminating account of Halley's life and science, making this a unique and highly readable biography of one of the key figures of his time.




Seventeenth-Century Indivisibles Revisited


Book Description

The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus. The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it. The list of authors involved in indivisibles ́ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.







Treatise on Conic Sections


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Revisiting the Foundations of Relativistic Physics


Book Description

2) the globalization of capital has far outstripped the ability of current labor movements, organized at best on a national level, to conduct an effective defense of the interests of labor within capitalism, let alone to seriously challenge the cap italist system. To develop some form-or forms--of international organization of labor, long an ideological challenge ("Workers of the World Unite") has now become an urgent matter of survival for the labor movements of the world. Here is a challenge, on which I think broad agreement is possible: Even those who think capitalism is capable of indefinite survival must agree that it has functioned best in the past-for example, during the long period of post-World War II expansion when the power of capital has been effectively limited by the countervailing power of labor. Effective exercise of that power has always depended on overcoming the seg mentation of labor due to such factors as locality, race, gender, occupation, etc. , which stilIremain important. Above, I have singled out the two factors that today seem key to me: the split between mental and manual labor, and segmentation by nationality. Let all concerned about the current state of capitalism work to build up the countervailing power of labor, and let time show whether this results in nothing more than the better functioning of capitalism, or whether a new challenge to the system ultimately emerges.




The Leibniz-Clarke Correspondence


Book Description

In 1715 the German philosopher Leibniz warned his friend the Princess of Wales of the dangers posed to religion by Newton's ideas. This book presents extracts from Leibniz's letters to Newtonian scientist Samuel Clarke.