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Newton's Principia for the Common Reader [Minkštas viršelis]

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(, University of Chicago)
  • Formatas: Paperback / softback, 618 pages, aukštis x plotis x storis: 250x165x40 mm, weight: 1275 g, numerous line figures, frontispiece
  • Išleidimo metai: 03-Apr-2003
  • Leidėjas: Oxford University Press
  • ISBN-10: 019852675X
  • ISBN-13: 9780198526759
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 618 pages, aukštis x plotis x storis: 250x165x40 mm, weight: 1275 g, numerous line figures, frontispiece
  • Išleidimo metai: 03-Apr-2003
  • Leidėjas: Oxford University Press
  • ISBN-10: 019852675X
  • ISBN-13: 9780198526759
Kitos knygos pagal šią temą:
Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.

Representing a decade's work from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.

Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London (1953), the National Medal of Science in the United States (1966), and the Copley Medal from the Royal Society (1984). His many publications include Radiative transfer (1950), Hydrodynamic and hydromagnetic stability (1961), and The mathematical theory of black holes (1983), each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable.

Recenzijos

...a continuing source of pleasure, and a permanent reminder of its author, whom it was a privilege to know. * L. Mestel, Observatory * ...a very individual account, in which Chandrasekhar brings understanding, expertise, and sensitivity to bear on the problems of revealing Newton to the 'common reader'. The common reader must be prepared to work hard, however, though the rewards are great for the one who does so. * R. Penrose, Times Higher Education Supplement * The great joy of Chandrasekhar's book is that it repays all the attention one gives it...The veil of Newtonian obscurity is lifted and one begins to grasp the extent of Newton's achievement. * D. Hughes, Nature *

Acknowledgements xxi
Prologue xxiii
The beginnings and the writing of the Principia
1(16)
Introduction
1(1)
The plague years
1(6)
The year 1679
7(1)
The year 1684
7(3)
The years 1685--1686: the writing of the Principia
10(7)
Basic concepts: Definitions and Axioms
17(26)
Introduction
17(1)
Basic concepts: Definitions
17(5)
Definition I
17(1)
Definition II
18(1)
Definition III
18(1)
Definition IV
19(1)
Definition V
19(1)
Definition VI
20(1)
Definition VII
20(1)
Definition VIII
20(2)
Basic concepts: the Laws of Motion
22(8)
Law I
22(1)
Law II
23(1)
Law III
23(1)
Corollaries I-IV
24(3)
Lemma XXIII
27(2)
Corollaries V and VI
29(1)
The Scholium to the Laws of Motion
30(5)
Additional amplifications
35(8)
The proportionality of mass and weight and the experiments on the pendulums
35(1)
Proposition XXIV, Book II
35(2)
Maxwell's reformulation of Newton's Laws of Motion
37(4)
The Newtonian principle of relativity
41(2)
On the notion of limits and the ratios of evanescent quantities
43(14)
Introduction
43(1)
Lemma I
43(1)
Lemmas II--IV
44(3)
Lemmas V--VIII
47(3)
Lemmas IX and X
50(2)
Lemma XI
52(5)
On the motion of particles under centripetal attraction: an introduction to Newton's treatment
57(10)
Introduction
57(1)
The dynamics of a particle under a general law of centripetal attraction
58(3)
The conservation of angular momentum
58(1)
The law of areas
59(1)
The conservation of energy
60(1)
The equation governing r in the orbital plane
60(1)
The dynamics of a particle under the inverse-square law of attraction
61(3)
The Lenz vector and the Lenz equation
62(1)
Kepler's third law
63(1)
An alternative derivation of the elliptical orbit
64(1)
The accelerations and velocities along a curved orbit
64(3)
The law of areas and some relations which follow
67(26)
Introduction
67(1)
The area theorem
67(9)
Proposition I
67(2)
Corollaries I--VI
69(1)
Proposition II
70(1)
Corollaries I and II
70(1)
Proposition III
71(1)
Corollaries I--IV
71(1)
Proposition IV
72(1)
Corollaries I--IX
73(2)
Proposition V
75(1)
Newton's relations for determining the law of centripetal attraction from the orbit
76(7)
Proposition VI
76(1)
Corollaries I--V
77(2)
Proposition VII
79(1)
`The same otherwise'
80(1)
Corollaries I--III
80(2)
Proposition VIII
82(1)
Two simple illustrations of the basic relation
83(10)
Proposition IX
83(2)
`The same otherwise'
85(1)
Lemma XII
86(1)
Proposition X
86(2)
`The same otherwise'
88(1)
Corollaries I and II
89(4)
The motion of bodies along conic sections
93(21)
Introduction
93(1)
Proposition XI
93(4)
`The same otherwise'
96(1)
Proposition XII
97(1)
`The same otherwise'
98(1)
Proposition XIII: the motion of a body along a parabola
98(5)
Lemmas XIII and XIV
98(2)
Proposition XIII
100(2)
Corollaries I and II
102(1)
Kepler's third law: Propositions XIV and XV
103(1)
Proposition XIV
103(1)
Proposition XV
104(1)
Corollary I
104(1)
Amplifications: Proposition XVI
104(10)
Proposition XVI
104(1)
Corollaries I--IX
105(2)
Proposition XVII
107(3)
Corollaries I--IV
110(2)
Scholium
112(1)
A personal reflection
113(1)
Supplement: on dual laws of centripetal attraction
114(229)
A recapitulation
114(5)
A digression
115(1)
The orbit described is an ellipse
115(1)
The orbit described is a hyperbola
116(1)
A body orbiting the conjugate hyperbola with the centre of attraction at S
117(1)
The self-duality of the inverse-fifth power law of attraction
117(2)
The mapping of orbits described in the complex plane
119(3)
The dual laws of centripetal forces
122(5)
Kepler's equation and its solution
127(16)
Introduction
127(1)
Kepler's equation
128(2)
Proposition XXX
130(3)
Corollaries I--III
132(1)
Lemma XXVIII
133(6)
Proposition XXXI
139(4)
Scholium
141(2)
The rectilinear ascent and descent of bodies
143(22)
Introduction
143(1)
An ab initio treatment of rectilinear motion
143(5)
The elliptic case
144(1)
The hyperbolic case
145(2)
The parabolic case
147(1)
The velocity of the body
148(1)
Proposition XXXII
148(2)
Proposition XXXIII
150(4)
A personal reflection
153(1)
Proposition XXXIV
153(1)
The reduction of the problem of rectilinear motion to one in circular motion
154(6)
Proposition XXXV
154(1)
Case I
155(1)
Case II
156(1)
Proposition XXXVI
157(1)
Proposition XXXVII
158(2)
A pause
160(1)
Proposition XXXVIII
160(1)
Corollaries I and II
161(1)
The initial-value problem
161(4)
Proposition XXXIX
161(2)
Corollaries I--III
163(2)
The conservation of energy and the initial-value problem
165(18)
Introduction
165(1)
The energy integral
165(3)
Proposition XL
165(3)
Corollaries I and II
168(1)
Proposition XLI
168(4)
Corollaries I and II
172(1)
The mystery of the missing corollary
172(2)
Motion under an inverse-cube law of centripetal attraction
174(6)
Some observations
179(1)
Proposition XLII
180(3)
On revolving orbits
183(18)
Introduction
183(1)
The theorem of revolving orbits
184(1)
Proposition XLIII
184(3)
Proposition XLIV
187(5)
Corollaries I--VI
189(3)
Proposition XLV
192(9)
Examples 1--3
194(2)
Corollaries I and II
196(5)
A pause
201(4)
Introduction
201(1)
Proposition XLVI
201(4)
Proposition XLVII
203(2)
The two-body problem
205(14)
Introduction
205(1)
The two-body problem: the general theorems
206(7)
Proposition LVII
206(2)
Proposition LVIII
208(1)
Corollaries I--III
209(1)
Proposition LIX
210(1)
Proposition LX
211(1)
Proposition LXI
212(1)
Initial-value problems
213(2)
Proposition LXII
213(1)
Proposition LXIII
214(1)
The solution of a many-body problem
215(4)
Proposition LXIV
215(4)
The method of the variation of the elements of a Kepler orbit and Newton's lunar theory: an introduction to Propositions LXV--LXIX
219(16)
Introduction
219(1)
The basic equations, definitions, and the coordinate system adopted
219(4)
The variation of the elements
223(5)
Variation of h
223(1)
Variation of ι
223(1)
Variation of Ω
224(1)
Variation of e
224(1)
Variation of ω = (ν, e)
225(1)
Variation of a and n
226(1)
Variation of Kepler's equation
227(1)
Summary
228(1)
Application of the method of the variation of the elements to lunar motion
228(7)
The disturbing function
229(1)
The components of F( = (Fr, Fα, Fh))
230(3)
Application of the variational equations
233(2)
The three-body problem: the foundations of Newton's lunar theory
235(34)
Introduction
235(1)
Proposition LXV
235(2)
Cases I and II
236(1)
Corollary III
236(1)
Proposition LXVI
237(2)
Cases I and II
237(2)
Proposition LXVI (continued): Corollaries I--VI
239(8)
The perturbing function
239(2)
The centripetal attraction
241(1)
The perturbed orbit
242(1)
The variation of the `constant of areas'
243(1)
The determination of x
243(1)
Corollaries I--VI
244(3)
Proposition LXVI (continued): Corollaries VII and VIII---the rotation of the line of apsides
247(3)
Corollary VII
247(3)
Corollary VIII
250(1)
Proposition LXVI (continued): Corollaries IX--XVII
250(9)
Corollary IX: the variation of the eccentricity
250(2)
Corollary X: the variation of the inclination
252(2)
Corollary XI: the variation of the direction of the ascending node (Ω)
254(1)
Corollary XII
255(1)
Further elaborations: Corollaries XIII--XVII
256(1)
Corollary XIII
256(1)
Corollary XIV
257(1)
Corollary XV
257(1)
Corollary XVI
257(1)
Corollary XVII
257(1)
A personal reflection
258(1)
Proposition LXVI (continued): Corollaries XVIII--XXII
259(6)
Corollary XVIII
260(1)
Corollary XIX
260(2)
Corollary XX
262(1)
Corollary XXI
263(1)
Corollary XXII
263(2)
Propositions LXVII--LXIX
265(4)
Corollary
265(1)
Proposition LXIX and Corollaries I and II
265(2)
Corollary III
267(1)
Scholium
267(2)
`The superb theorems'
269(34)
Introduction
269(1)
Scholium
269(1)
Propositions LXX--LXXII
269(6)
Proposition LXX
269(1)
Proposition LXXI
270(3)
A personal reflection
273(1)
Proposition LXXII
273(2)
Corollary III
275(1)
Propositions LXXIII--LXXV
275(5)
Proposition LXXIII
275(1)
Proposition LXXIV
276(2)
Corollary III
278(1)
Proposition LXXV
278(1)
Corollaries I--IV
279(1)
Proposition LXXVI
280(3)
Corollaries I--IX
281(2)
Propositions LXXVII and LXXVIII
283(4)
Proposition LXXVII
283(1)
Cases 1--6
283(3)
Proposition LXXVIII
286(1)
Corollary
286(1)
Scholium
286(1)
Lemma XXIX and Propositions LXXIX--LXXXI
287(6)
Examples 1--3
291(2)
Proposition LXXXII and the discovery of the method of inversion and the principle of images
293(5)
Proposition LXXXII
294(2)
On the discovery of the method of images
296(1)
Method of Inversion
297(1)
Propositions LXXXIII and LXXXIV
298(4)
Proposition LXXXIII
298(1)
Proposition LXXXIV
299(1)
Scholium
299(3)
Some personal reflections
302(1)
Attraction by non-spherical bodies
303(20)
Introduction
303(1)
How we may discriminate between different laws of centripetal attraction
303(3)
Proposition LXXXV
304(1)
Proposition LXXXVI
305(1)
The scaling law
306(1)
Proposition LXXXVII and Corollary I
306(1)
Corollary II
307(1)
Propositions LXXXVIII and LXXXIX
307(2)
Proposition LXXXVIII
307(1)
Corollary
308(1)
Proposition LXXXIX
308(1)
Corollary
309(1)
The attraction by circular discs and round solids at points along their axes
309(4)
Proposition XC
309(1)
Corollaries I--III
310(1)
Proposition XCI
311(1)
Corollary I
312(1)
Corollaries II and III of Proposition XCI and Proposition XCII
313(4)
Corollary II
313(3)
Corollary III
316(1)
Proposition XCII
317(1)
Proposition XCIII
317(6)
Cases 1 and 2
318(1)
Corollaries I--III
319(1)
Scholium
320(3)
A digression into Opticks
323(20)
Introduction
323(1)
Propositions XCIV--XCVI
323(4)
Proposition XCIV
324(2)
Proposition XCV
326(1)
Proposition XCVI
326(1)
The Scholium
327(2)
The ovals of Descartes
329(5)
Proposition XCVII
329(1)
Corollary I
330(1)
A Comment
331(1)
Corollary II
331(1)
Proposition XCVIII
332(2)
The concluding Scholium of Book I
334(9)
Scholium
334(1)
Appendix I. An analytic solution for the ovals of Descartes
334(4)
Appendix II. Maxwell on the ovals of Descartes
338(2)
Postscript
340(3)
Introduction to Newton's System of the World (Book III)
343(194)
Prolegomenon
345(8)
Rules of reasoning in philosophy
345(1)
Phenomena
346(2)
Propositions
348(5)
The universal law of gravitation
353(28)
Introduction
353(2)
Propositions and rules (to which references are made)
353(2)
Propositions I--III
355(2)
Proposition IV and the Moon test
357(4)
Scholium
360(1)
The emergence of the law of gravitation
361(1)
Proposition V
361(1)
Scholium
362(1)
Proposition VI: the confirmation of the equality of the inertial and the gravitational masses by astronomical data
362(8)
Proposition VI
362(7)
Corollaries I--V
369(1)
Proposition VII: the universal law of gravitation
370(1)
Corollaries I and II
370(1)
Propositions VIII and IX: the implications of the `superb theorems'
371(4)
Proposition VIII
371(1)
Corollaries I--IV
372(2)
Data
374(1)
Mass
374(1)
Mean density
374(1)
Surface gravity
374(1)
Corollary IV
374(1)
Proposition IX
375(1)
Propositions X--XIV
375(6)
Proposition X
375(1)
Hypothesis I
376(1)
Proposition XI
376(1)
Proposition XII
377(1)
Corollary
378(1)
Proposition XIII
378(1)
Proposition XIV
379(1)
Scholium
379(2)
The figure of the Earth and of the planets
381(18)
Introduction
381(1)
Proposition XVIII and the historical background
381(3)
Proposition XIX: the method of the canals
384(10)
Newton's method of the canals
384(2)
What Newton withheld
386(3)
Newton's determination of g(ob)pole/g(ob)eq and ε/m
389(3)
Application to the figure of Jupiter
392(2)
The variation of gravity over an oblate spheroid
394(5)
Proposition XX
394(2)
A personal reflection
396(3)
On the theory of tides
399(20)
Introduction
399(2)
A recapitulation
401(2)
The tidal force of a distant body acting on the boundary of a spherical body
401(2)
Proposition XXIV: an annotated version
403(8)
Propositions XXV, XXXVI, and XXXVII
411(4)
Proposition XXV
411(1)
Proposition XXXVI
412(1)
Corollary
413(1)
Proposition XXXVII
414(1)
Appendix: the equilibrium theory of the tides
415(4)
The lunar theory
419(36)
Introduction
419(1)
Propositions XVII and XXI
420(1)
Proposition XVII
420(1)
Proposition XXI
420(1)
Propositions XXII and XXIII
421(2)
Proposition XXII
421(2)
Proposition XXIII
423(1)
Proposition XXVI
423(2)
Proposition XXVII
425(1)
Proposition XXVIII
425(1)
Proposition XXIX
426(4)
The variation in the ascending node, Ω: Proposition XXX
430(4)
Proposition XXX
430(3)
Corollary I
433(1)
Corollary II
434(1)
Proposition XXXI
434(7)
Newton's procedure
436(3)
Newton's transformation of the equation dΩ/dt for a Kepler ellipse
439(2)
Propositions XXXII and XXXIII
441(2)
Proposition XXXII
441(2)
Proposition XXXIII
443(1)
The variation of the inclination
443(5)
Proposition XXXIV
444(1)
Corollaries I--III
445(1)
Corollary IV
446(1)
Proposition XXXV
446(2)
Scholium
448(7)
The annual equation
449(1)
The motion of the apogee and the `Portsmouth equation'
450(5)
The precession of the equinoxes
455(22)
Introduction
455(1)
On the precession of the equinoxes: a current treatment
456(10)
Euler's equations
458(1)
Euler's angles
459(1)
The equations governing precession and nutation
459(6)
The solar contribution to the precession
465(1)
The lunar contribution to the precession and the lunisolar precession
465(1)
Moment of momentum, moment of inertia, and circulation
466(6)
Lemma I
467(2)
Lemma II
469(1)
Lemma III
470(1)
Hypothesis II
471(1)
Proposition XXXIX: to find the precession of the equinoxes
472(3)
A personal reflection
475(2)
On comets
477(60)
Introduction
477(1)
Lemma IV and Proposition XL
478(3)
Lemma IV
478(2)
Proposition XL
480(1)
Corollaries I--IV
480(1)
Lemma V: Newton's theory of interpolation
481(19)
Newton's treatment in Methodus Differentialis
482(1)
Proposition 1
483(1)
Proposition 2
484(2)
A modern version of Proposition 2
486(2)
A modern version of Proposition 3
488(7)
Propositions 3--6
495(1)
Proposition 3: Cases 1 & 2
495(2)
Propositions 4--6
497(1)
Lemma V
498(2)
Lemmas VI--XI
500(14)
Lemma VI
500(1)
Lemma VII
501(1)
Lemma VIII
502(3)
Scholium
505(3)
Lemma IX
508(1)
Lemma X and `Lambert's theorem'
509(1)
Lemma X
509(2)
`Lambert's theorem'
511(2)
Lemma XI
513(1)
Propositions XLI and XLII
514(21)
Proposition XLI
514(1)
Recapitulation
515(1)
The formulation of the problem
516(1)
Newton's method of solution in the orbital plane
517(3)
Newton's formulation of the solution
520(10)
Proposition XLII
530(3)
Appendix
533(2)
The general Scholium
535(2)
Miscellanea
537(58)
The effect of air-drag on the descent of bodies
539(16)
Newton's problem and its solution
539(2)
Lemma III and Proposition XV
541(8)
Lemma III
541(2)
Proposition XV
543(3)
Corollary I
546(1)
Corollary II
546(1)
Corollary III
546(1)
Corollary IV
546(1)
Corollary V
547(1)
Corollary VI
547(1)
Corollary VII
547(2)
Corollaries VIII and IX
549(1)
Proposition XVI--XVIII
549(2)
Proposition XVI
549(1)
Corollary I
550(1)
Corollary II
550(1)
Corollary III
550(1)
Scholium
550(1)
Proposition XVII
550(1)
Proposition XVIII
551(1)
An alternative method of solution of Newton's problem
551(4)
The solid of least resistance
555(16)
Introduction
555(1)
Proposition XXXIV
556(2)
The Scholium, I: the frustum of minimum resistance
558(1)
The Scholium, II: the solid of least resistance
559(8)
Newton's manner of solution
562(5)
Amplifications
567(4)
Newton's kernel-function
567(1)
The Euler-Lagrange equations
567(1)
The Legendre test
568(1)
The Weierstrass test
569(2)
The problem of the brachistochrone
571(8)
Introduction
571(2)
Newton's anonymous solution
573(2)
The solution derived from its extremal property
575(4)
Newton's manner of solution
577(2)
The velocity of sound and of long waves in canals
579(16)
Introduction
579(1)
Propositions XLI--XLIII: Newton's conception of wave propagation
580(1)
Propositions XLIV--XLVI: the propagation of long waves in canals
581(5)
Proposition XLIV
581(1)
Corollary I
582(1)
Corollary II
582(1)
Corollary III
583(1)
Proposition XLV
583(1)
Proposition XLVI
583(1)
Corollary I
584(1)
Corollary II
584(1)
The theory of long waves in canals
584(2)
A standard treatment of the velocity of sound
586(1)
Propositions XLVII--L
587(4)
Proposition XLVII
588(1)
Proposition XLVIII
589(1)
Proposition XLIX
589(1)
Proposition L
590(1)
Scholium
591(4)
Epilogue 595