Essay Review: Newton's Principia : Introduction to Newton's ‘Principia’,Isaac Newton's ‘Philosophiae Naturalis Principia Mathematica’

This edition traces, for the first time, the path from M to E₁, noting all additions made in the course of printing and distinguishing those made by Halley from those made by Newton himself. Rigaud S. P. (1838) is the only previous scholar to have paid any attention to Edleston M. J. (1850) documented Cotes's role in the improvements made in E₂, Brewster D. (1855) described some of the changes in E₂ and E₃, while Rouse-Ball W. W. (1893) recognized the need for a variorum edition and Hall A. R. (1958) has traced some of the changes introduced in Book II of the printed editions of the Principia.

The references by author and date are to items in the bibliography at the end of the Introduction.

This copy, identified by the press-mark N.14.4, lacks the ‘privilege’, which, the editors note, has been taken from a copy in the Library of Trinity College, Cambridge, identified by the press-mark NQ.17.34. It is greatly to be desired that all editors of facsimile editions would follow this example in reproducing an exact facsimile and identifying the copies used. On the recent ‘facsimile’ of the French edition of the Marquise du Chastellet, see Cohen (1969a).

For a complete definition of variant reading, describing the exact sense of the general statement, the reader is referred to the editors' “Guide to the Apparatus criticus” which precedes the text.

Cohen discusses the origin of this mistake in his Introduction, p. 85, but he has inadvertently interchanged ‘plana’, the correct word, with ‘plano’, the incorrect word. It must have been the last letter of ‘plana’, coming at the fold, that was misread as ‘plano’ and written thus in M and copied in E₁ and E₂.

See McGuire J. E. , “Atoms and the analogy of nature; Newton's third rule of philosophizing”, Studies in history and philosophy of science, i (1970), 3–58.

See Koyré and Cohen (1960). Recent papers on Newton and the aether include Hawes J. L. , “Newton and the ‘Electric Attraction Unexcited’”, Annals of science, xxiv (1968), 121–30; Hawes J. L. , “Newton's revival of the aether hypothesis and the explanation of gravitational attraction”, Notes and records of the Royal Society of London, xxiii (1968), 200–12; Rosenfeld L. , “Newton's views on aether and gravitation”, Archive for history of exact sciences, vi (1969), 29–37; Aiton E. J. , “Newton's aether-stream hypothesis and the inverse square law of gravitation”, Annals of science, xxv (1969), 255–60.

Of particular interest is the lengthy insert between pp. 412 and 413 of E₁ dealing with the knowledge of the ancients. See Cohen (1964) and McGuire and Rattansi (1966).

Herivel (1965) gives an account of Newton's dynamical researches in the period 1664–84, which draws on the manuscripts in the Portsmouth Collection. The present Introduction, it should be remembered, is primarily concerned with the development of Newton's ideas shown in the successive changes introduced in the Principia.

At the conclusion of Problem 4 (De motu), Newton remarks that a body subject to an inverse-square central force may also move in a parabola or a hyperbola. In the Principia, Book I, Proposition 13, Corollary 1, Newton concluded that an inverse-square orbit must be a conic section. In E₂ he added the following explanation:

For the focus, the point of contact, and the position of the tangent being given, a conic section may be described, which at that point, shall have a given curvature. But the curvature is given from the centripetal force and the bodies velocity given: And two orbits mutually touching one the other, cannot be described by the same centripetal force and the same velocity (Motte's translation).

See also Whiteside D. T. , “The mathematical principles underlying Newton's Principia Mathematica”, Journal for the history of astronomy, i (1970), 116–138, p. 134, ref. 33.

This has been pointed out several times. See Koyré (1965), 183; Lohne (1960), 17 and 23; Aiton E. J. , “Kepler's second law of planetary motion”, Isis, lx (1969), 75–90, p. 76.

The value of the intermediate manuscripts may be illustrated by the example of Newton's description of vis insita in De motu corporum, which contains the phrases later used in a letter to Bentley where he refers to the impossibility that “Gravity should be innate, inherent and essential to matter”.

Whiteside D. T. , “The mathematical principles underlying Newton's Principia mathematica”, 119.

In his review of the Principia in the Philosophical transactions, having described the first eleven propositions (concerning Kepler's laws), Halley writes: “All which being found to agree with the Phenomena of Celestial Motions, as discovered by the great Sagacity and Diligence of Kepler, our Author extends himself upon the consequences of this sort of Vis centripeta …”. Cohen suggests that Halley is being critical, however mildly.

Leibniz's annotated copy of the Principia has recently been located in Switzerland. See Fellmann E. A. , “Die Marginalnoten von Leibniz in Newtons Principia Mathematica 1687”, Humanisms und Technik, xvi (1972), 110–28. See also Leibniz G. W. , Marginalia in Newtoni Principia Mathematica (Edition critique en langue allemande par E. A. Fellmann, traduction française de J. F. Courtine, Paris, 1973).

See £. Aiton J. , “Leibniz on motion in a resisting medium”, Archive for history of exact sciences, ix (1972), 257–274.

See Aiton E. J. , The vortex theory of planetary motions (London and New York, 1972), ch. 6.

See Cohen I. B. , “Newton's second law and the concept of force in the Principia”, The annus mirabilis of Sir Isaac Newton 1666–1966 (edited by Palter R. , Cambridge, Mass. and London, 1970), 143–85. See also Hankins T. L. , “The reception of Newton's second law of motion in the eighteenth century”, Archives Internationales d'histoire des sciences, xx (1967), 43–65.

In E₂ Newton deduces the principle of universal gravitation from the vis centripeta of the planets using Regula III, which states: “The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever”.

Cotes would have preferred to sign a preface written by either Newton or Bentley.

Cohen shows that LL consists of two manuscripts (or states), LLα. and LLβ. The first eight leaves of LLα (now lost) were replaced by twenty new leaves LLβ(1). LL is made up of LLβ(1); LLα, leaves 9–24, revised; LLα, leaves 25–32; LLβ, 56 leaves. This analysis completes and clarifies the analysis begun by Herivel (1965); the major difference concerns Herivel's division of Cohen's LLβ into two sections, which he supposed to have been written at different times.

The bibliography may be supplemented by the following items, which are additional to those cited in the notes above: Bork A. M. , “Logical structure of the first three sections of Newton's Principia”, American journal of physics, xxxv (1967), 342–44; Buchholtz Klaus-Dietwardt , Isaac Newton als Theologe (Witten, 1965); Butts R. E. and Davis J. W. (eds), The methodological heritage of Newton (Oxford, 1970); Churchill Mary S. , “The seven chapters, with explanatory notes”, Chymia, xii (1967), 27–57 (alchemical manuscript of Newton); Cronin J. L. and Jones L. C. , “Invariant velocity components: A key to Newton's analysis of Keplerian planetary motion”, American journal of physics, xxxv (1967), 219–23; Gabbey A. , “Force and inertia in seventeenth century dynamics”, Studies in history and philosophy of science, ii (1971), 1–67; Guerlac H. and Jacob M. C. , “Bentley, Newton and Providence”, Journal of the history of ideas, xxx (1969), 307–18; Hawes J. L. , “Newton's two electricities”, Annals of science, xxvii (1971), 95–103; Hofmann J. E. , “Neue Newtoniana”, Studia Leibnitiana, ii (1970), 140–5; Home R. W. , “The third law in Newton's mechanics”, British journal for the history of science, iv (1968), 39–51; Kargon R. , “Newton, Barrow and the hypothetical physics”, Centaurus, xi (1965), 45–56; Kubrin D. , “Newton and the cyclical cosmos: Providence and the mechanical philosophy”, Journal of the history of ideas, xxviii (1967), 325–46; Lawrence P. D. and Molland A. G. , “David Gregory's Inaugural Lecture at Oxford”, Notes and records of the Royal Society of London, xxv (1970), 143–178; McGuire J. E. , “Force, active principles and Newton's invisible realm”, Ambix, xv (1968), 154–208; Metzger Hélène , Attraction universelle et religion naturelle chez quelques commentateurs anglais de Newton (Paris, 1938); Trengrove L. , “Newton's theological views”, Annals of science, xxii (1966), 277–94; Westfall R. S. , Force in Newton's physics (London and New York, 1971); Whiteside D. T. , “Before the Principia”, Journal for the history of astronomy, i (1970), 5–19.