The Mathematical Principles of Natural Philosophy... Translated... by Andrew Motte. To which are added, the lawes of the moon’s motion, according to gravity. By John Machin... In two volumes.

London: for Benjamin Motte, 1729.

First edition in English of the Principia, the magnificent Jones-Macclesfield large paper copy in contemporary morocco; with its important provenance, this is surely the most desirable copy in private hands. The first edition was published in Latin in 1687 and “is generally described as the greatest work in the history of science. Copernicus, Galileo and Kepler had certainly shown the way; but where they described the phenomena they observed, Newton explained the underlying universal laws. The Principia provided the greatest synthesis of the cosmos, proving finally its physical unity. Newton showed that the important and dramatic aspects of nature that were subject to the universal law of gravitation could be explained, in mathematical terms, with a single physical theory. With him the separation of the natural and supernatural, of sublunar and superlunar worlds disappeared. The same laws of gravitation and motion rule everywhere; for the first time a single mathematical law could explain the motion of objects on earth as well as the phenomena of the heavens. The whole cosmos is composed of inter-connecting parts influencing each other according to these laws. It was this grand conception that produced a general revolution in human thought, equalled perhaps only by that following Darwin’s Origin of Species… [Newton] is generally regarded as one of the greatest mathematicians of all time and the founder of mathematical physics” (PMM 161). This first English translation, published two years after Newton's death, was prepared by Andrew Motte (1696-1734), the son of the publisher Benjamin Motte Sr. and brother of the printer Benjamin Motte Jr. The translation is based on the 1726 third edition of the Latin text, edited by Henry Pemberton, and is dedicated to Sir Hans Sloane as President of the Royal Society. The first book, De Motu Corporum (On the motion of bodies), applies the laws of motion to the behaviour of bodies in various orbits. The second book continues with the motion of bodies in fluids and with the behaviour of fluids themselves. In the third book De Mundi Systemate (On the system of the world) Newton applies the Law of Universal Gravitation to the motion of planets, the Moon and comets. Newton derives Kepler's laws of planetary motion from this system and shows how a range of phenomena are governed by the same set of natural laws, including the behaviour of Earth's tides and the precession of the equinoxes, although Newton failed to account fully for the irregularities in the Moon’s motion caused by the gravitational influence of the Sun.

Provenance: William Jones (1675-1749) – one page of manuscript notes in ink referring to Proposition XC, Problem XLIV, probably in Jones’s hand, loosely inserted at vol.1 pp. 300-301; George Parker, 2nd Earl of Macclesfield (1697-1764), armorial bookplate (dated 1860) and small blind-stamp to title and preliminary leaves in each volume.

“If, in midsummer 1684, Newton had any plans for the publication of a work of mathematics or natural philosophy, his attention was probably focused on one of two possible subjects. The first of these was the treatment of the geometry of curved lines, on which he had recently been working; the second concerned his discoveries in the manipulation of infinite series and the invention of the calculus … By autumn 1684, however, Newton’s attention was concentrated elsewhere, in an attempt to prove that the planets move in elliptical orbits as a result of the constant action of a force inversely proportional to the square of their distance from the sun. This sudden change of emphasis had been provoked by a visit from Edmond Halley (1656–1742), which probably took place in August. Halley may have met Newton in 1682, shortly after he returned to England from a journey through France and Italy. Halley’s account of making the earliest evening observation of the comet of 1680 on the road to Paris certainly found its way into Newton’s ‘Waste Book’ around this time. Halley had been elected to the Council of the Royal Society in 1683, and, when he called on Newton, he told him about a conversation that he had had with Robert Hooke and Sir Christopher Wren at a meeting of the Society on 14 January 1684. Hooke had claimed to be able to demonstrate that an inverse square law governed celestial mechanics. In response to this boast, Wren had set a challenge by offering a prize to the first of his companions who could prove the operation of this law.

“Newton had been interested in the motion of heavenly bodies since the mid-1660s. The idea of the inverse square law was in many ways a natural development of Johannes Kepler’s laws of planetary motion, by then quite well known in England, in the light of Cartesian thinking about the force possessed by a body in motion. Descartes’ influence was certainly apparent in the papers on motion that Newton composed in the late 1660s and early 1670s. In one of these, Newton had invoked Kepler’s third law and extrapolated from it to an inverse square law applying to the ‘endeavour [conatus] in the principal planets of receding from the sun’. He subsequently told both Halley and David Gregory that he had composed these words in 1673, before the publication of Christiaan Huygens’ thoughts on the subject. Wren had discussed the possible operation of an inverse square law with Newton in 1677 and Hooke had touched on it in an exchange of letters with Newton between November 1679 and January 1680 … it later appeared that Hooke’s prompting played a significant role in encouraging Newton once more to think seriously about the behaviour of bodies moving under gravity.

“Thus, when Halley told him about Hooke’s boasting in 1684, Newton was able to claim that he could now provide the necessary proof that an inverse square law governed the motion of the planets. Unfortunately, it turned out that he was unable to find where he had written this proof down. Nevertheless, by November, Newton had sent Halley a new tract, ‘De motu’, in which he had already extended his earlier thoughts. Newton realised that not just the planets but all heavenly bodies were governed by the same principles of force. Moreover, he had introduced for the first time an absolute notion of force, as distinct from the Cartesian notion that force might be relative to the body being moved. Despite the excitement that ‘De motu’ generated at the Royal Society, it was only a beginning. For the next year and a half, Newton worked furiously to clarify his definitions and to extend his calculations to heavenly bodies other than planets. Here, the observations of a comet that he had made in 1664 were put to work alongside the more detailed information that he had amassed about the comet of 1680 …

“On 28 April 1686, the Royal Society received the text of Book I of the Principia. Despite the prolonged absence of many members of its Council, the Society decided on 19 May that it should publish Newton’s work. Halley, who was now the Society’s Clerk, was ‘intrusted to look after the printing it’. He immediately wrote to Newton on 22 May to consult him about publication and to warn him that Hooke had ‘some pretension upon the invention of [the] rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center. He sais you had the notion from him, though he owns the Demonstration of the Curves generated thereby to be wholly your own.’ Newton’s reply dismissed Hooke’s claims and he welcomed the first proofs that Halley sent him in June. But the prospect of bitter controversy made Newton anxious about some of what he had written. On 20 June he wrote to promise Halley the text of Book II of the Principia, which he had finished the previous summer, but warned ‘I designed [the] whole to consist of three books … The third wants [the] Theory of Comets. In Autumn last I spent two months in calculations to no purpose for want of a good method, [which] made me afterwards return to [the] first Book & enlarge it [with] divers Propositions … The third I now designe to suppress.’ He continued: ‘Philosophy is such an impertinently litigious Lady that a man had as good be engaged in Law suits as have to with her. I found it so formerly & now I no sooner come near her again but she gives me warning.’

“The final form of the Principia owed much to Halley’s tact and patience. He encouraged Newton to persevere with Book III and waited quietly for its arrival. He supervised the printer and designed the woodcuts to illustrate the text. He tolerated Newton’s further delays, agreeing to his desire that the completion of the book be postponed until at least late spring 1687. Above all, Halley accepted the costs of the publication of the book himself. The Royal Society was at the time as good as bankrupt, reduced to paying its officers, including Halley, in unsold copies of the lavish History of Fishes that it had published in 1686. Moreover, Halley’s position had come under threat at the Society’s elections, perhaps as a result of lobbying by Hooke …

“Despite the acclaim that greeted his achievements, however, Newton still felt that there was more to be done. A particular problem remained the explanation of universal gravitation. Newton’s treatment of gravity had been one of the revolutionary aspects of his work. By showing that its effects could account in detail for the movements of the heavens, Newton had been able to give universal force to the laws of motion that he propounded. Yet, in the eyes of many of his most distinguished contemporaries, his achievement was qualified by the failure to provide a properly philosophical account of gravity. Newton could describe the effects of gravitation but he could not explain them adequately. Newton’s friend, Nicolas Fatio de Duillier, felt that he had the answer and, for a time in the early 1690s, it seemed possible that he might produce a new edition of the Principia. Others of Newton’s growing band of young disciples, particularly David Gregory, also discussed his plans to augment the work” (Footprints, pp. 87-91).

In the event, the second edition of Principia did not appear until twenty-six years after the first. 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). The third edition, published in 1726 and edited by Henry Pemberton (1694-1771), contains only minor changes from the second, the most significant perhaps being the inclusion of the tract ‘The motion of the Moon’s nodes’ by the brilliant John Machin (1680-1751) who, Newton said, understood the Principia better than anybody.

“Motte’s achievement [in completing the first English translation of the Principia] is somewhat surprising as it was widely assumed that Pemberton, ideally placed in 1727 as the editor of Principia (1726) and self-proclaimed confidant of the aging Newton, would produce such a work. It was an assumption shared by Henry Pemberton himself. As early as March 1727, almost before Newton was cold, he announced his plans. They were repeated in the preface to his A View of Sir Isaac Newton’s Philosophy (1728). Motte first publicly announced his plans in the Journal des sçavans for June 1727 and repeated them in England the following year.

“The race was clearly on and both contestants lost no time in claiming for their unfinished works the special authority which only Newton’s name could provide. Motte made the most unlikely claim that his translation had been made ‘sous les yeux et suivant les avis be M. Newton.’ Pemberton, probably with more justification, responded by insisting that his work contained ‘sans doute vrai sens de l’auteur.’

“That the outsider Motte completed his translation first suggests strongly that he had begun the enterprise long before Newton’s death. The fact that he used earlier Principia editions in his translation reinforces this view and suggests that he began his work, at least in a preliminary way, before the appearance of the third edition in 1726.

“Having won the race, Motte was unwilling even to recognize Pemberton’s existence. His name was omitted from the acknowledgements Newton made in the preface to Principia (1726). Also, with an elaborate dedication to Sir Hans Sloane, President of the Royal Society, Motte was clearly seeking to bestow on the work an authority it neither needed nor had earned.

“In addition to Motte’s translation the work also includes a translation of Newton’s System of the World. Whether this is by Motte is unclear” (Gjertsen, pp. 478-479). The System of the World, first published in Latin in 1728, is the second book of the earliest draft of Principia, which differs very substantially from the version finally published in 1687. Far from being simply an extract from Principia, The System of the World includes several discoveries and observations that were omitted from Principia itself. There is a technique which can be counted “as the first acceptable determination of a star’s distance” (North, p. 418); and, centuries ahead of his time, “Newton points to the possibility of Terrestrial Tidal effects, which were discovered by Michelson in 1919, and in another passage indicates the existence of the planet Uranus, which was actually first seen by Herschel in 1781” (Babson).

In addition, Motte’s translation includes John Machin’s ‘The laws of the Moon’s motion according to gravity,’ published here for the first time. “Machin was probably closely involved in the preparation of the translation. One of the mysteries of the work is an appendix claiming to contain ‘explications (given by a friend) of Some Propositions in the Book, not demonstrated by the Author.’ The eight-page appendix then proceeds to explicate Book I, prop. 91, cor. 2 and the Scholium to Book II, prop. 34 by showing how, for example, fluxions can be used to find the force of attraction of a sphere. The author was undoubtedly knowledgeable about Newton’s work, for the material included in the appendix is similar to papers in the [Portsmouth Collection] only recently published. Motte is unlikely to have had any such access to Newton’s thought and papers. Machin, on the other hand, was highly thought of by Newton and could well have had access to his unpublished papers.

“The work has been so successful that later scholars have been deterred from attempting a rival translation. They have settled instead for ‘revisions’ and ‘corrections’ … When Cohen and Koyre were considering attempting for the first time in 250 years to add to their critical edition of Principia a new English translation, they concluded eventually that, although Motte sometimes translated too freely, interpolated his own expressions, mixed editions, and used unfamiliar expressions, he remained ‘sound, literate and generally accurate’” (Gjertsen, pp. 479-480).

This book almost certainly derives from the collection of William Jones. This is true of many of the books in the Macclesfield library, but the Jones provenance is particularly appealing when found in the works of Newton. Jones first came to Newton’s attention through the publication of his Synopsis palmariorum matheseos (1709), which gave an account of fluxions (and introduced the symbol π for the ratio of the circumference to the diameter of a circle). In 1708 Jones had acquired the bulk of the papers and correspondence of John Collins (1625-83), including Collins’ transcription of De analysi, Newton’s earliest manuscript on calculus. Jones was keen to publish this, and other mathematical papers of Newton he had acquired from Collins. The priority dispute with Leibniz over the invention of calculus being still very much alive, it was to Newton’s advantage to have some of his earlier work on calculus in print, and he allowed Jones to publish De analysi, with some of his other mathematical writings, as Analysis per quantitatum series (1711). Jones dutifully recorded in the introduction his opinion, undoubtedly suggested by Newton, that the bulk of the results had been established by 1665 and 1666. Jones further aided Newton by serving on the committee set up by the Royal Society in 1711 to settle the priority dispute with Leibniz. Inevitably, Jones agreed with his colleagues that Newton's work was by far the earlier. Jones also acquired an exceptional collection of Newton’s autograph manuscripts, which were left at Shirburn at his death and are now in Cambridge University Library.

Babson 20; Norman 1587; Wallis 23; Cohen, ‘Pemberton's translation of Newton's Principia, with notes on Motte’s translation’, Isis 54 (1963), 319-51. See PMM 161. North, Cosmos: An Illustrated History of Astronomy and Cosmology, 2008.



Two vols., 8vo (227 x 130mm), pp. [38], 320, [2], 393, [13], viii, 71, [1], with 2 engraved frontispieces by A. Motte, 2 folding letterpress tables, 47 folding engraved plates (numbered 1-25, 1-19 and 3 unnumbered), and 3 engraved head-pieces by Motte. The frontispiece to volume I shows the apotheosis of Newton, and quotes four lines from Halley's liminary verses to the original edition of Principia, that to volume II shows a pendulum and has two references to the text, one in the scholium generale. Contemporary black morocco, gilt roll-tooled border to sides, spines in six compartments with raised bands, red morocco lettering pieces, red edges, preserved in modern black cloth slipcases (very minor wear to bindings).

Item #5105

Price: $195,000.00