- Weinstock , Robert . 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 610 – 617 .
- Weinstock , R. 1989 . Long-buried Dismantling of a Centuries-old Myth: Newton's Principia and Inversesquare Orbits . American Journal of Physics , 57 : 846 – 849 .
- Weinstock , R. 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 613 – 613 .
- Weinstock , R. 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 611 – 611 .
- Cajori , Florian , ed. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World 56 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- Cajori , Florian , ed. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World 61 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- Hall , A. Rupert and Tilling , Laura , eds. 1975 . The Correspondence of Isaac Newton Vol. v , 5 – 6 . New York 1709–13
- Koyré , Alexandre and Cohen , I. Bernard , eds. 1972 . Isaac Newton's Philosophae Naturalis Principia Mathematica, The Third Edition With Variant Readings Vol. I , 125 – 125 . Cambridge, Mass.
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 61 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 5 – 6 . Berkeley, California translated into English by Andrew Motte in 1729
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 56 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 61 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- See Newton I. Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Cajori Florian Berkeley, California 1946 68 108 translated into English by Andrew Motte in 1729 where Newton constructs conic-sections satisfying a variety of given conditions. Also see The Mathematical Papers of Isaac Newton, Volume iii, edited by D. T. Whiteside (Cambridge, 1974), pp. 151–95, for some of Newton's work on curvature.
- Weinstock , R. 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 611 – 611 .
- Weinstock , R. 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 615 – 615 .
- Weinstock , R. 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 613 – 613 .
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 40 – 43 . Berkeley, California translated into English by Andrew Motte in 1729
- For the present purposes, we must determine whether Newton could have proved GAP, keeping to a level of rigour consistent with the Principia. Thus it is certainly not enough to know that GAP is intuitively obvious, as ‘intuitively obvious’ statements in mathematics often turn out to be false or to be true but difficult to prove (at the appropriate level of rigour). To see an attempt to deal with GAP which relies solely on geometric and physical intuition, read Stehle Philip Comment on Weinstock's objection to Newton's logic American Journal of Physics 1983 51 199 199
- Cushing , James T. 1982 . Kepler's Laws and Universal Gravitation in Newton's Principia . American Journal of Physics , 50 : 617 – 628 . See especially p. 623
- Cushing , James T. 1982 . Kepler's Laws and Universal Gravitation in Newton's Principia . American Journal of Physics , 50 : 623 – 623 .
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 61 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 134 – 134 . Berkeley, California transalted into English by Andrew Motte in 1729
- Weinstock . 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 611 – 611 .
- Weinstock . 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 613 – 613 .
- Weinstock , R. 1989 . Long-buried Dismantling of a Centuries-old Myth: Newton's Principia and Inversesquare Orbits . American Journal of Physics , 57 : 848 – 848 .
- For an illuminating and scholarly discussion of the difficulties inherent in evaluating the scientific work of a different age, explore Kuhn Thomas S. The Structure of Scientific Revolutions , second edition Chicago 1970
- Newton did his work in one world—a particular collection of assumptions, notations, concepts, definitions, rules, habits of mind, priorities and preconceptions—and we do ours in another. Thus a translation of text in the Principia into modern mathematics must always be an imperfect reflection of Newton's work. Still, with sufficient care and attention, one can sometimes translate quite faithfully—witness Cushing's article Cushing James T. Kepler's Laws and Universal Gravitation in Newton's Principia American Journal of Physics 1982 50 617 628 a lucid modern translation of Newton's work on Kepler's laws and universal gravitation. One might even say that Cushing's article, at least in one place, is a bit too faithful, for his translation of Newton's argument in Corollary I contains the same gap as the original! He constructs the correct conic-section, but never produces on that conic the required motion, namely, a motion about the focus. This is somewhat ironic, since Cushing's article appeared alongside Weinstock's 1982 article (footnote 1) in the American Journal of Physics presumably in part to offer a contrasting view of Newton's argument in Corollary I. Yet Cushing's paper ends up reinforcing two of Weinstock's points: Newton's argument in Corollary I does contain a gap, and in the wrong light, this gap can be very hard to see.
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 61 – 61 . Berkeley, California translated into English by Andrew Motte in 1729
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 133 – 133 . Berkeley, California translated into English by Andrew Motte in 1729
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 134 – 134 . Berkeley, California translated into English by Andrew Motte in 1729
- Weinstock , R. 1982 . Dismantling a Centuries-old Myth: Newton's Principia and Inverse-square Orbits . American Journal of Physics , 50 : 615 – 615 .
- Newton , I. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Edited by: Cajori , Florian . 109 – 116 . Berkeley, California translated into English by Andrew Motte in 1729
- Cajori , Florian , ed. 1946 . Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World 40 – 43 . Berkeley, California translated into English by Andrew Motte in 1729
- Quoted from Ward Geoffrey C. A First-Class Temperament: The Emergence of Franklin Roosevelt New York 1989 xv xv
- On this issue of priority, consult Aiton Eric J. The Contributions of Isaac Newton, Johann Bernoulli and Jakob Hermann to the Inverse Problem of Central Forces Studia Leibnitiana 1987 17 47 58 Sonderheft See also E. J. Aiton, ‘The Solution of the Inverse Problem of Central Forces in Newton's Principia’, Archives internationales d'Histoire des Sciences, 38 (1988), 271–6. The first paper presents an elegant and scholarly account of the solutions to the Inverse Problem proposed by Newton, Bernoulli, and Hermann. Both papers contain brief comments on Weinstock's objection to Newton's argument.
Annals of Science
Volume 48, 1991 - Issue 2