Philosophiae naturalis principia mathematica. Editio secunda auctior et emendatior.

Cambridge: [Cornelius Crownfield at the University Press], 1713.

The important second edition of “the greatest work in the history of science” (PMM). This is a fine copy in an unrestored contemporary binding. The Principia elucidates the universal physical laws of gravitation and motion which lie behind phenomena described by Newton's predecessors Copernicus, Galileo and Kepler. Newton establishes the mathematical basis for the motion of bodies in unresisting media (the law of inertia); the motion of fluids and the effect of friction on bodies moving through fluids; and, most importantly, sets forth the law of universal gravitation and its unifying role in the cosmos. “For the first time a single mathematical law could explain the motion of objects on earth as well as the phenomena of the heavens … It was this grand conception that produced a general revolution in human thought, equalled perhaps only by that following Darwin's Origin of Species” (PMM). Published twenty-six years after the first, this second edition of Newton’s Principia was printed at the Cambridge University Press, which Richard Bentley had recently revived. Edited by Roger Cotes (1682-1716), it contains his important preface in which he attacks the Cartesian philosophy “and refutes an assertion that Newton’s theory of attraction is a causa occulta” (Babson). There is also a second preface by Newton, and substantial additions, the chapters on the lunar theory and the theory of comets being much enlarged. But the most important addition is the Scholium generale, which appears here in print for the first time. “The General Scholium, added to the Principia in 1713, is probably Newton’s most famous writing … In this text, Newton not only challenges the natural philosophy of Descartes, counters criticism levelled against him by Leibniz and appeals for universal gravitation and an inductive method, but he embeds a subversive attack on the doctrine of the Trinity, which he believed was a fourth-century corruption of Christianity” (The Newton Project).

“In 1709 Cotes became heavily involved in the preparation of the second edition of Newton’s great work on universal gravitation, the Philosophiae naturalis principia mathematica. The first edition of 1687 had few copies printed [about 250]. In 1694 Newton did further work on his lunar and planetary theories, but illness and a dispute with Flamsteed postponed any further publication. Newton subsequently became master of the mint and had virtually retired from scientific work when Bentley persuaded him to prepare a second edition, suggesting Cotes as supervisor of the work.

“Newton at first had a rather casual approach to the revision, but Cotes took the work very seriously. Gradually, Newton was coaxed into a similar enthusiasm; and the two collaborated closely on the revision, which took three and a half years to complete. The edition was limited to only 750 copies, and a pirated version printed in Amsterdam [in 1714] met the total demand” (DSB, under Cotes)

“The most significant feature remains the number of changes introduced into the edition. Rouse Ball (An Essay on Newton’s Principia,’ 1893) noted that, of the 494 pages of Principia (1687), ‘397 are more or less modified in the second edition.’ Changes include ‘the propositions on the resistance of fluids, Book II, section VII props 34 - 40; the lunar theory in Book III; the propositions on the precession of the equinoxes, Book III. prop. 39; and the propositions on the theory of comets, Book III, props. 41, 42’. In addition there was a completely new Scholium generale. Also included for the first time were a table of contents (Index capitum totius opera) which did no more than list the section headings of the first two books, and a rather sketchy index (Index rerum alphabeticus). Cotes also provided an important preface in which he undertook to explain and defend Newton's account of gravity” (Gjertsen, Newton Handbook, pp. 475-6).

“When the question of a Preface arose early in 1713, Cotes was initially in some doubt what to include. He first thought of an attack on Leibniz’s dynamical treatise Tentamen (1689), but much preferred an alternative proposal that either Newton or Bentley should prepare a Preface that Cotes would then loyally ‘own … and defend’. Bentley, however, told Cotes that he should undertake the task himself, while Newton, after some initial hesitation, warned Cotes to ‘spare ye name of M. Leibniz’. He also declined to read it before its publication. He informed Newton that he would ‘add something … concerning the manner of Philosophising’ and indicate in particular how the Newtonian approach differed from the Cartesian.

“Cotes has been accused, with some justification, of misrepresenting Newton’s notion of gravity. Unaware of Newton’s Letter to Boyle (1679) and his Letters to Bentley (1694), he spoke witheringly of those who ‘would have the heavens filled with a fluid matter’, while of gravity he insisted that it was just as much a primary property of bodies as ‘extension, mobility, and impenetrability’. Yet, to Bentley, Newton had insisted: ‘You sometimes speak of gravity as essential and inherent to matter. Pray, do not ascribe that notion to me’ (Correspondence, III, p. 240). Earlier, to Boyle, he had spoken of an ‘etherial substance’ diffused through all space. Oddly enough Newton accepted the misrepresentation of his views without complaint, public or private.

“On two other topics Cotes was more accurate. The first was a strong attack launched against Cartesian physics in general and the vortex theory of planetary motion in particular. The second was a commitment to providentialism, with the claim that 'this world, so diversified with that variety of forms and motions we find in it, could arise from nothing but the perfectly free will of God directing and presiding over all'.

“The General Scholium … was sent to the editor, Roger Cotes, on 2 March 1713 with the comment: ‘I intended to have said much more about the attraction of the small particles of bodies, but upon second thoughts I have chosen rather to add but one short Paragraph about that part of Philosophy’ (Edleston, Correspondence of Sir Isaac Newton and Professor Cotes, 1850, p. 147) …

“One reason for the new Scholium was to answer criticisms raised by Leibniz and Berkeley against the general cosmology of Principia. Newton had been accused, for example, of presenting God as no more than an incompetent watchmaker incapable of making a clock which did not need his regular attention each time it broke down. Newton chose to reply by presenting in some of his finest prose his own conception of God. It is not a creed many Christians today will find attractive.

“Newton rejected the idea that the true nature of God consisted in his possession of the familiar attributes of perfection; it lay rather in his ‘dominion’. For, he declared, ‘a being, however perfect, without dominion, cannot said to be Lord God’. We may well admire him for his perfections but ‘we reverence and adore him on account of his dominion’. Further, this dominion was exercised 'in a manner not at all human … in a manner utterly unknown to us'. We know God only through his works, ‘by his most wise and excellent contrivances of things’. There seems little room in Newton’s austere theology for anything like a personal God. Indeed, he went out of his way to dismiss such an option. God, he insisted, ‘is utterly void of all body and bodily figure, and can therefore neither be seen, nor heard, nor touched’. From God, Newton turned to gravity. In often-quoted words, he declared his failure to have discovered any cause for gravity. As, he insisted, ‘I frame no hypotheses’, any attempt to speculate about possible causes had no place in experimental philosophy; ‘it is enough’, he concluded the point, ‘that gravity does really exist, and act according to the laws which we have explained’. The Scholium concluded with an intriguing paragraph, presumably the item referred to in the letter to Cotes above. He spoke of ‘a most subtle spirit which pervades and lies hid in all gross bodies’. It is through this spirit, Newton proposed, that bodies cohere, ‘light is emitted, reflected, refracted, inflected, and heats bodies’, sensations are excited, electric bodies repel and attract, and the will operates. A formidable list, and one demanding some explanation. Newton merely concludes, however: ‘But these are things that cannot be explained in few words’” (Gjertsen, pp. 463-4).

“The difficult style of the General Scholium reflects two dynamics in particular: first, some of the ideas present in this document were considered controversial and even heretical; second, Newton believed that his readers could be divided into two camps, the vulgar (who are not be able to understand higher truths) and the cognoscenti (who are). Newton was primarily interested in reaching those in the latter category. In order to deal with the first dynamic and to achieve the goal of the second, Newton deliberately constructed this document so that the uncontroversial and more broadly acceptable ideas appeared on the outer or “open” layers, while the specialised meanings for the adepti were concealed in the inner or “closed” layers, which are increasingly difficult to penetrate without specialised or privileged knowledge. For example, virtually all readers recognised and accepted Newton’s natural theological argument in the fourth paragraph, but only a select few recognised the attack on the doctrine of the Trinity in the fourth through sixth paragraphs (which was precisely Newton’s aim). The General Scholium is constructed much like a Russian doll and, accordingly, restricts access to its ultimate meaning. In using this strategy, Newton more closely resembles the ancient Pythagoreans, who hid higher theological and philosophical truths in similitudes and riddles, than a modern scientist (which Newton was not). When interpreting the General Scholium, it is important to take into account several backdrops: Newton’s attack on Descartes’ method and physics, Leibniz’s contention that Newton’s conception of an intervening God was weak, and the controversy surrounding the publication of Newton’s follower Samuel Clarke’s critique of the doctrine of the Trinity in 1712. In the General Scholium, Newton takes the dangerous step of supporting several arguments outlined in Clarke’s book. Denial of the Trinity was illegal in Britain until 1813, a full century after the General Scholium first appeared. Thus, the most revolutionary and important book in the history of science, championed by the orthodox British establishment throughout the eighteenth century and beyond, ends on a subversive note” (The Newton Project).

“Printed in an edition of 750 copies, it was sold in quires for 15s and bound for a guinea. Bentley's accounts have survived and show that the total cost of the printing came to £117 4s 1½d. He sold 375 copies to various booksellers and individuals at an average cost of 13s each. The printer C. Crownfield took a further 200 copies at 11s each. This yielded Bentley a profit of £200 while still holding a substantial stock for future sale. Some of these were in fact presentation copies. Twelve were given to Cotes and a further six to Newton. There is also a distribution list in Newton's papers of another seventy or so recipients. It covers most of the great libraries, scientific institutions and Courts of Europe. Individuals listed include Cassini, de la Hire, Varignon, Bernoulli, Leibniz and Machin. But even this list is incomplete as it contains no reference to the copies known to have been presented by Newton to Queen Anne personally on 27 July 1713, nor a copy he sent to Yale University” (Gjertsen, pp. 475-6).

Babson 12; ESTC T93210; PMM 161 (for the first edition); Wallis 8.

4to (239 x 190 mm), pp. [xxviii], 484, [8], with engraved device on title, folding engraved plate of the cometary orbit at page 465, woodcut diagrams throughout. Contemporary half vellum , a 7cm split to the lower rear hinge, corners with slight wear. A very light water stain to upper right margin of final 20 leaves, otherwise fine a fresh.

Item #4606

Price: $45,000.00

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