De mundi systemate liber.
London: J. Tonson, J. Osborn & T. Longman, 1728. First edition of Newton’s rarest book — the discarded first draft of what would become Book III of Principia, posthumously published in the year following his death — and an extraordinary association copy in contemporary panelled calf, inscribed on the front pastedown by James Stirling: “Ja: Stirling Ex Dono Dni De Moivre”. The inscription records the gift, in the year of publication, from Abraham de Moivre to Stirling, his junior by twenty-five years. The two men were the foremost mathematicians at work in London at Newton’s death and the leading contemporary proponents of Newtonian mathematics; both had been part of Newton’s personal circle for decades, both were Fellows of the Royal Society in his lifetime, and within two years of the present gift their joint correspondence on the asymptotic behaviour of the binomial coefficient would yield what is now known as Stirling’s formula. Of de Moivre, the ODNB remarks that he was the man “whose early investigations led Stirling into this topic”. The book passed with the rest of Stirling’s mathematical library into the family seat at Garden House in Stirlingshire, where it remained for nearly three centuries until the dispersal at Lyon & Turnbull, Edinburgh, on 23 October 2025. No comparable association copy of the Latin first edition is recorded in the modern trade. The text Conduitt brought through the press in 1728 had been written in 1685, in the same Cambridge year as the first two books of Principia, and was originally intended to constitute the second of two books under the title De motu corporum liber secundus. By the summer of 1685 Newton had expanded the design of Principia to three books, with the original second book becoming the third; at the same moment he reconsidered the character of the new Book III. He had at first envisaged a popular treatment that, as he noted in the introduction to the published Book III, ‘might be read by many’; but, fearing the controversies such a work would invite, he replaced the popular draft with a strictly mathematical exposition that could be read only by those who had mastered the first two books (Gjertsen, p. 573). Having no immediate use for the rejected version, Newton had Humphrey Newton (no relation, his Cambridge amanuensis) make a fair copy of part of the manuscript, and on 29 September 1687 deposited it in the Cambridge University Library in the supposed fulfilment of his obligations as Lucasian Professor: that deposit, mostly in Humphrey’s hand, is now ULC MS Add. 3990. A further copy by Roger Cotes is preserved at Trinity College, Cambridge, and a third copy is held at Clare College; Ernst Weil offered a fourth in his Catalogue 27 (no. 152). Newton’s distaste for controversy precluded the printing of any of these copies in his lifetime. The 1728 publication was arranged by John Conduitt, the husband of Newton’s half-niece Catherine Barton and his successor as Master of the Mint, who had taken charge of Newton’s manuscripts after his death in March 1727. Conduitt sold the deposit copy to the bookseller Jacob Tonson for thirty-one pounds and ten shillings, and Tonson published in partnership with John Osborn and Thomas Longman. It was almost certainly Conduitt who substituted the title De mundi systemate for Newton’s own De motu corporum liber secundus — a definite improvement, corresponding much more closely to the content, but one that has caused enduring confusion with the title of the published Book III of Principia, from which the present text differs sharply in style and method. What is published here differs from the printed Book III of 1687 not only in style but in substance. The first part offers a non-mathematical account of centripetal force; the next turns to the dynamics of the solar system; two long discussions then follow on the theory of tides and the nature and dynamics of comets, the work closing with the inverse problem of recovering a comet’s orbit from its observed velocity and distance from the Sun. Several discoveries and observations preserved in the rejected text never reached the printed Principia at all. Pages 3–4 contain Newton’s thought-experiment of the orbiting cannonball, with an accompanying diagram (here Tab. I, Fig. 1) showing that there is no kind-difference between projectile and orbital motion: a ball fired from the top of a mountain with progressively greater velocity falls further and further from the base of the mountain until at length it never reaches the ground at all and enters into orbit. Ernst Weil regarded this as “the anticipation of an artificial satellite, 270 years before its advent”. The discussion and diagram do not appear in the 1687 Principia in any form. More substantial still is the discussion of stellar distances, on which the printed Principia is virtually silent. Newton had investigated the question in 1685 by a method devised by James Gregory in 1668: comparing the brightness of the Sun, by way of its reflection from Saturn, with that of a fixed star, and then applying the inverse-square law of photometry. With assumptions about the nature of reflection, the absence of light-loss in interstellar space, and the equality of intrinsic brightness between the Sun and the comparison star, Newton found Sirius to lie at a distance of about a million astronomical units. The figure is too great by an order of magnitude, but, as J. D. North has argued, this can be counted as “the first acceptable determination of a star’s distance” (Cosmos, p. 418). Newton’s motivation was theological as much as astronomical: he had been perplexed by the question why the cosmos did not collapse upon itself under the action of universal gravitation, and the immense interstellar distances supplied a workable answer. The text further records, in advance of their observational confirmation, two phenomena that would not be detected for another two centuries. Newton points to the possibility of terrestrial tidal effects; these were observed by Albert A. Michelson and Henry G. Gale at Yerkes Observatory in 1919, by the application of monochromatic interference fringes to a determination of the rigidity of the Earth, and reported in Science 50, pp. 327–8. In another passage, first identified by J. Ph. Wolfers in his German Principia of 1872, Newton indicates the possible existence of a planet beyond Saturn, ultimately observed by Herschel in 1781 and named Uranus — ironically, Herschel himself, on first observation, took it to be a comet, the very class of body that Newton, throughout the present work, regards as continuous with the planets and as moving on closely related orbits. The publication history of 1728 is further complicated by the simultaneous appearance of an anonymous English translation, A Treatise of the System of the World, sometimes attributed to Andrew Motte, the translator of Principia in 1729; its translator has never been certainly identified. The Latin and English texts diverge in important respects, and it is unclear whether the Treatise is a translation of a different (and now-lost) manuscript or whether the differences reflect interpolations by the translator. The Latin version is unambiguously based on the manuscript in Humphrey’s hand: the compositor uses a half-square bracket in the margins to mark the end of one page and the beginning of another in the manuscript, and to flag in some places the start of a manuscript signature (Cohen, p. xii). The translator additionally suppressed Newton’s many citations to specific propositions in the original-draft Principia, sometimes adversely affecting the readability of the result; in the Latin, the citations have been preserved, but updated to correspond to the proposition numbering of the third edition of Principia (London, 1726), which makes the present Latin text the more informative scientifically and historically. The citations were restored only in the second English edition of 1731, an edition that I. B. Cohen accordingly considered “of far more value … than the first” English version (Cohen, p. xiii). The Treatise is much more frequently encountered in commerce: OCLC lists more than fifty copies of the English first edition, and twenty-five or more have appeared at auction. The Latin first edition presents a quite different picture. The Latin De mundi systemate is exceptionally rare. OCLC lists only six copies worldwide, three of them in North America (Chicago, the Huntington Library — the Babson copy — and Yale), and no copy is recorded in either the Cambridge College libraries or the Cambridge University Library, despite Newton’s manuscript residing on the same site. The Cambridge Digital Library editorial note to MS Add. 3990 states, in a small error perhaps connected to the Cambridge gap, that the work was first published in 1731 — the year of the second edition. Auction appearances over the last fifty years have been restricted to two recorded copies: the Honeyman copy, rebacked and damp-stained, and the Macclesfield copy from the Earls of Macclesfield’s celebrated mathematical library at Shirburn Castle. The present copy is the third copy to come to public sale in that period, and is the first to be offered with a contemporary presentation inscription linking it directly to two of Newton’s closest mathematical contemporaries. The Latin text was reprinted in London in 1731 and again in Amsterdam in 1742; it was incorporated into Johannes Castillioneus’s Isaaci Newtoni Opuscula at Lausanne in 1744 and into Samuel Horsley’s five-volume Isaaci Newtoni Opera at London in 1779–85; none of these later printings carries the textual authority of the 1728 first edition, prepared in the immediate aftermath of Newton’s death from the manuscript his executors retained. James Stirling (1692–1770), to whom the present copy was given, was born at Garden House in Stirlingshire on 11 May 1692, the third son of Archibald Stirling and Anna Hamilton, into a Scottish family with deep Jacobite sympathies. He matriculated at Balliol College, Oxford on 18 January 1711 as a Snell Exhibitioner from the University of Glasgow, and held a Bishop Warner Exhibition from October of the same year. His Jacobite associations cost him both scholarships and his place at Oxford in 1715, when he refused to swear the oaths of allegiance and abjuration following the rising of 1715. Stirling travelled to the Continent — reaching Venice by 1717 — where he supported himself by teaching mathematics, and where in the same year he published his first major work, Lineae Tertii Ordinis Neutonianae, a treatise on the cubic curves that completed and extended Newton’s classification appended to Opticks in 1704. The book was dedicated to Newton, with whom Stirling had begun corresponding from Venice through Newton’s Royal Society colleagues, and it secured Stirling’s standing in the British mathematical community despite his political exile. By 1725 Stirling had returned to London, with Newton’s personal assistance, and was appointed to the staff of William Watts’s Academy in Little Tower Street, off Covent Garden — one of the leading commercial training schools of the city, where Stirling’s 1727 syllabus advertised lectures on mechanical and experimental philosophy spanning mechanics, hydrostatics, optics, and astronomy. Newton proposed Stirling for fellowship of the Royal Society; he was elected on 3 November 1726, four months before Newton’s death. Throughout his London decade Stirling was a frequent visitor to the aged Newton at his country house at Kensington: “Sr Isaac Newton lives a little way off in the country”, he wrote to Maclaurin in 1725, finding Newton kind and serviceable but much enfeebled. The fruit of these London years was Stirling’s second and most famous work, Methodus Differentialis (London, 1730), the early classic of numerical analysis containing what are now known as Stirling numbers, Stirling’s interpolation formula, and the asymptotic formula for the logarithm of the factorial that bears his name. Abraham de Moivre (1667–1754), the donor, had reached England as a Huguenot refugee in 1685 following the Revocation of the Edict of Nantes, and supported himself in London by tutoring the sons of the gentry and by giving mathematical lessons in the coffee-houses of St Martin’s Lane. He had become a friend of Newton by about 1692, and was elected Fellow of the Royal Society in 1697. He saw Samuel Clarke’s Latin Optice through the press in 1706, the year following Opticks in English; in 1712 he served on the Royal Society’s commission, alongside Halley, Arbuthnot, Jones, Machin and others, that arbitrated the priority dispute between Newton and Leibniz over the calculus and adjudicated in Newton’s favour. De Moivre’s own publications — De Mensura Sortis (1711); The Doctrine of Chances in three editions (1718, 1738, 1756); Miscellanea Analytica (1730); the formula linking complex exponentials to trigonometry and the early statement of the central limit theorem — placed him among the foremost probabilists of his century. The story preserved by his Royal Society colleagues that the aged Newton would direct mathematical questioners to him with the words “he knows all these things better than I do” was already current in his lifetime. The friendship between Stirling and de Moivre was the closest mathematical relationship of the older man’s last decades, and the most consequential of Stirling’s. Stirling’s letter to de Moivre of 19 June 1729, preserved in the Royal Society archives and reproduced in Ian Tweddle’s annotated translation of Methodus Differentialis (Springer, 2003), illustrates how Stirling had calculated the coefficient of the middle term of the binomial expansion (a + b)n for large n by means of a logarithmic series; de Moivre, who had pursued the same problem for some years, was able to extend his earlier results using Stirling’s ideas, and shortly afterwards published a Supplement to his Miscellanea Analytica. By September 1730 Stirling was relating the new exchange to Gabriel Cramer at Geneva. The joint provenance of the asymptotic formula for n!, named after Stirling but resting on de Moivre’s earlier “Approximatio ad summam terminorum binomii”, has its origin in this exchange. The Methodus Differentialis of 1730, which states the formula in ‘Example 2 to Proposition 28’, was published two years after the present gift; the book Stirling received from de Moivre in 1728 carried the work of their common master, the rejected first draft of Principia, into the next mathematical generation. The dating of the inscription is precise. The Latin De mundi systemate, published in London in the second half of 1728, would have come into the hands of the leading London mathematicians within weeks of issue; de Moivre’s presentation to Stirling, recorded in Stirling’s own hand on the front pastedown, can therefore be placed in the closing months of 1728 or in early 1729, in the year following Newton’s death and within two years of Stirling’s election to the Royal Society. The form of the inscription is the recipient’s record of the gift, not the donor’s presentation: it is unsigned by de Moivre, and the courtesy form “Dni De Moivre” (Domini De Moivre) is the standard early-eighteenth-century Latin used between Fellows. The hand is the same as that of Stirling’s 1729 letter to de Moivre and of his autograph manuscript of Methodus Differentialis, both preserved at Garden House until the same dispersal of October 2025. The book is in entirely original condition, in the contemporary panelled calf binding it received in London in 1728: the covers framed by double gilt fillets enclosing a recessed central panel, the spine in compartments separated by raised bands, the red morocco lettering-piece preserving the gilt label ‘DE MUNDI SYSTE | MAT’ with characteristic compartment dotted ornament, and the edges sprinkled red. It travelled with Stirling from London to Garden House in or about 1735, when he relinquished his London teaching to take up the management of the Scots Mining Company at Leadhills in Lanarkshire, an appointment he held until his retirement; the books and instruments he had assembled in his London years went with him, were preserved by his collateral heirs (Stirling died unmarried in Edinburgh on 5 December 1770), and remained at Garden House through nine generations of the Stirling family until the dispersal at Lyon & Turnbull on 23 October 2025. In the same sale, Stirling’s autograph Methodus Differentialis manuscript brought £50,400, his own annotated copy of Principia £42,840, and the Edinburgh silver pocket microscope by John Clark used in his Leadhills assays a further £42,840: the present De mundi systemate stands within the same archive of working tools by which one of Newton’s leading disciples carried his mathematics into the next century. 4to (231 × 177 mm), pp. iv, 108, with two folding engraved plates of geometrical diagrams (Tab. I and Tab. II), title printed in red and black with engraved typographic ornament. Contemporary panelled calf, covers framed by double gilt fillets enclosing a recessed central panel, spine in six compartments with five raised bands, red morocco lettering-piece preserving gilt ‘DE MUNDI SYSTE | MAT’, edges sprinkled red. Covers rubbed with surface wear to the recessed central panels, spine and joints sound, lettering-piece intact.
Item #6610
Price: $65,000.00
