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WINCKLER, Johann Heinrich; WATSON, William; NEWTON, IsaacLivre Rare Book

Thomas Newton; (Shepard Kollock, printer)Biblio.com

Dissertations on the Prophecies Which have been remarkably fulfilled and at this time are fulfilling in the World in two volumes

1787WE22795Elizabethtown NJ: Shepard Kollock 1787. Leather_bound. Good. Two volumes octavo in original plain brown calf hubbed spines spine labels. 412 and 439 pp. with index in Volume II verso of final leaf is adverts. Both volumes are firm in their bindinsg; they show heavy use aith rounding to the extremities and rubbing to the spines some discoloration to the boards. Couple stains to the title page of Vol. I and fingering to the title page of Vol. II. Scattered foxing. Volume I has an inscription on the front free endpaper: "Union Library W. Simsbury No.7/ Bo't March 8th 1791 price 7/6"d/ Meetings 3rd Tuesdays in June 7 Sept/ at 4PM also/ 3rd Tuesdays in Dec & March 9 o'clock PM". Shepard Kollock 1750-1839 was one of New Jersey's earliest printers and editors; his press was located in Elizabethtown. He founded the New Jersey Journal New Jersey's third newspaper in 1779 it continued to be printed later as the Elizabeth Daily Journal for 212 years. He learned his trade in Philadelphia but had to relocate to the West Indies for his health and continued to print there. When news of Lexington and Concord reached him he returned to New Jersey joinging the Continental Army as a Lieutenant he saw action in the Battle of Trenton and other engagements. Resigning his commission in 1779 he was urged by the Continental Congress to start a newspaper the aforementioned New Jersey Journal. Located in Chatham it was an extremely important orgas as Kollock received news directly from Washington's headquarters located just a few miles away in Morristown. After the war the paper renamed the Elizabeth Daily Journal editorialized in favor of Jefferson Madison and Monroe. Kollock printings are highly sought after by collectors. Shepard Kollock unknown

The Old Book Shop of Bordentown (ABNJ) · États-Unis195,00 $US≈ 164,99 €

Thomas NewtonBiblio.com

Newton on the Prophesies. Volumes 2 and 3.

1787FB60 (1 & 2) /8Tan calf spine with black title plates and gilt title. Green cloth boards. Two volumes only. Measurements are for one volume. Although part of a broken set these later two volumes are a meaningful adjunct to any library. In his day Newton's writings were well accepted – today they are more often seen as an example of man's gullibility. Thomas Newton 1 January 1704 – 14 February 1782 was an English cleric biblical scholar and author. He served as the Bishop of Bristol from 1761 to 1782. Newton was educated at Trinity College Cambridge and was subsequently elected a fellow of Trinity. He was ordained in the Church of England and continued scholarly pursuits. His more remembered works include his annotated edition of Paradise Lost including a biography of John Milton published in 1749. In 1754 he published a large scholarly analysis of the prophecies of the Bible titled Dissertations on the Prophecies. In his 1761 edition of Milton's poetry he gave the title On His Blindness to Sonnet XIX When I Consider How My Light is Spent. Newton was appointed the Bishop of Bristol in 1761 and in 1768 became the Dean of St Paul's Cathedral in London. He has been considered a Christian universalist. One of Newton's famous quotes concerns the Jewish people: The preservation of the Jews is really one of the most signal and illustrious acts of divine Providence. and what but a supernatural power could have preserved them in such a manner as none other nation upon earth hath been preserved. Nor is the providence of God less remarkable in the destruction of their enemies than in their preservation. We see that the great empires which in their turn subdued and oppressed the people of God are all come to ruin. And if such hath been the fatal end of the enemies and oppressors of the Jews let it serve as a warning to all those who at any time or upon any occasion are for raising a clamor and persecution against them. Rebound John Rivington hardcover

Martin Frost · Royaume-Uni375,00 £GB≈ 428,17 €

NEWTON, Sir IsaacBiblio.com

Arithmetica Universalis; sive de Compositione et Resolutione Arithmetica Liber. Ciu accessit Helleiana Aequationum Radices Arithmetice Inveniendi Methodus .

17225823London: Benji & Sam. Tooke 1722. Second edition. Second edition but the first authorised and edited by Newton probably with the assistance of John Machin of his treatise on algebra or 'universal arithmetic' his "most often read and republished mathematical work" Whiteside. "Included are 'Newton's identities' providing expressions for the sums of the ith powers of the roots of any polynomial equation for any integer i plus a rule providing an upper bound for the positive roots of a polynomial and a generalization to imaginary roots of René Descartes' Rule of Signs" Parkinson.. NEWTON'S ALGEBRA - THE FIRST EDITION AUTHORISED AND EDITED BY NEWTON. Second edition but the first authorised and edited by Newton probably with the assistance of John Machin - see below of his treatise on algebra or 'universal arithmetic' his "most often read and republished mathematical work" Whiteside Papers V p. xiv. "Included are 'Newton's identities' providing expressions for the sums of the ith powers of the roots of any polynomial equation for any integer i pp. 251-2 plus a rule providing an upper bound for the positive roots of a polynomial and a generalization to imaginary roots of René Descartes' Rule of Signs pp. 242-5" Parkinson p. 138. About this last rule for determining the number of imaginary roots of a polynomial which Newton offered without proof Gjertsen p. 35 notes: "Some idea of its originality . can be gathered from the fact that it was not until 1865 that the rule was derived in a rigorous manner by James Sylvester." The work is a printed version of lectures Newton prepared in the period 1672-83. Although the editor of the first edition William Whiston later claimed that he had Newton's permission to print the lectures Newton was far from satisfied with the result complaining that the titles and headings were not his and that it contained numerous mistakes. His real concern was that "an unfinished text composed so long before should now be presented to the world as though it represented his latest researches into the structure and applications of algebra" Papers V p. 11 and that Whiston had "too faithfully and impercipiently followed the parent manuscript incorporating in his princeps edition its several inconsistencies and lapses into error without in the main even bringing them to the reader's notice . In his private library copy of the edition Newton corrected many minor misprints inserted more appropriate running heads 'Multiplicatio' 'Divisio' 'Extractio Radicum' 'De Forma Aequationis' 'Reductio Aequationum' 'Resolutio Quaestionum Arithmeticarum Geometricarum' and the like and on the Arithmetica page 279 deleted an unwarranted half-title 'Aequationum Constructio linearis'; more radically he mapped out a large-scale reordering of the sixty-one geometrical problems comprising its central portion seeking to grade them into a more logical sequence and in increasing levels of difficulty while in the concluding section on the 'curvilinear ' construction of equations he pared away all not directly needed flesh reducing it to two skeletal conchoidal neuses now denuded of their proof. That last savage act of butchery apart all these improvements were incorporated in the Latin revise - future parent and rightfully so of all subsequent editions - which he himself brought to publication in 1722" ibid. pp. 13-14. Babson notes that "This edition was the last issued during Newton's lifetime and is almost as rare as the first." In commerce this edition is in fact much rarer than the first: ABPC/RBH list only two other copies of this edition since 1975 but ten of the first. "In fulfilment of his obligations as Lucasian Professor Newton first lectured on algebra in 1672 and seems to have continued until 1683. Although the manuscript of the lectures in Cambridge University Library carries marginal dates from October 1673 to 1683 it should not be assumed that the lectures were ever delivered. There are no contemporary accounts of them and apart from Cotes who made a transcript of them in 1702 they seem to have been totally ignored. Whiteside Papers V p. 5 believes that they were composed 'over a period of but a few months' during the winter of 1683-4" Gjertsen pp. 33-4. The Arithmetica "derives partly in its discussion of the elemental algebraic operations and of the reduction and exact solution of equations from Newton's earlier unpublished 'Observations' on the introduction to Cartesian algebra presented by Gerard Kinckhuysen in his 1661 Stelkonst partly in its techniques for delimiting the number and nature real or complex of the roots of equations and for reducing these by factorization from his own independent researches as a young postgraduate student into the theory of equations and partly in its approximate geometrical construction of cubics from his previously elaborated 'Problems for construing aequations'. Apart from novelties in detail and the fabrication of new illustrative 'questions' what is most notable is Newton's developing awareness - still far from completely expressed - of the fundamental structural equivalence which exists between the elements constants and free variables and their functional relationships of algebra and those given lines and undetermined line-lengths and their coordinate interconnections of geometry and his deepening grasp of the still more general isomorphism which permits a two-way 'translation' between mathematical 'speech' and the 'language' of exact science in all its manifestations. His guiding doctrine that algebra is 'universal arithmetick' embroiders a theme stated briefly in an opening phrase of his 1671 treatise on infinite series and fluxions and expounded in a geometrical context earlier still in preface to James Gregory's study of universal mathematical principles. Now also however he reaches tentatively forward to Barrow's notion that algebra is in its essence the abstract logic of relationships between quantities in divorce from their particular setting and hence to be developed as an independent metamathematical system" Papers V pp. 3-4. "We may reasonably conjecture that pressure was in some manner put upon Newton in late 1683 to fulfil however tardily his statutory obligation annually to deposit a fair copy of ten of his lecture scripts and be all but sure that the arrival in Cambridge the next spring of his young amanuensis Humphrey Newton able to take over from Isaac the dreary time-consuming chore of rewriting his much cancelled and corrected worksheets in legible and coherent form gave him new heart to codify and expand his previous mathematical investigations. But these surmises remain as unproved and essentially undemonstrable as the plausible suggestion that it was Edmond Halley's famous first visit to Cambridge in the late summer of 1684 to talk about the unsolved problem of elliptical planetary motion which provoked him abruptly to relinquish his restructuring of the Arithmetica. We may guess still more tenuously that the appearance in mid-1685 of John Wallis' voluminous Treatise of Algebra Both Historical and Practical would have long deterred Newton from making any efforts to have his own rival studies made publicly available. In later years certainly he grew increasingly soured with the often cumbersome computations and techniques of Cartesian algebra - at one point indeed if we may believe David Gregory he qualified it as 'the Analysis of the Bunglers in Mathematicks - and we may be certain that his reluctance during 1705-6 to have Whiston edit the deposited text of his algebraic lectures was not merely the manifestation of a growing personal antagonism to his successor in the Lucasian chair" ibid. pp. xi-xii. "When Newton resigned his Lucasian professorship to his deputy William Whiston in December 1701 it was natural that the latter should wish to familiarize himself with the deposited lectures of his predecessor. Whiston did not hesitate to introduce portions of Newton's earlier optical lectures concerning the mathematical theory of the rainbow into his own Lucasian Praelectiones physico-mathematica in the spring of 1706 and about that time also he turned his attention to the succeeding ones on algebra and began to consider their publication. In the meantime rumours began to spread in both Oxford and London that 'Newton's friends solicit him to publish a Treatise of Algebra which he wrote long since. If such ill-founded whispers penetrated to Cambridge Whiston ignored them and went quietly ahead arranging with the London stationer to underwrite the expense of printing the deposited manuscript and then subsequently between September 1705 and the following June correcting both specimen and proof sheets as they emerged from the compositor's bench at the University Press. In February 1706 David Gregory accurately noted in his memoranda that 'Its talked that there is now printing at Cambridge Elements or Principles of Algebra written long since by Sir Isaac Newton but withdrew his added remark that it was 'lately revised by him' when he saw Newton in London in July and was given a first-hand account of the history of the 'Algebra that is printing and near printed at Cambridge'. Though as Whiston was later to announce publicly Newton had given his reluctant approval for the edition . Despite its minor inconsistencies and confusions Gregory's report vividly conveys Newton's concern that an unfinished text composed so long before should now be presented to the world as though it represented his latest researches into the structure and applications of algebra" pp. 8-11. For a book that was to become Newton's most often republished mathematical work the Arithmetica initially made little impact in Britain and was not even graced by a review in the Philosophical Transactions. On the Continent the reception accorded the lectures was more positive. "Leibniz unhesitatingly divining their author beneath the cloak of anonymity gave them a long review in the Acta Eruditorum of Leipzig in 1708. Written thirty years before he noted and now deservingly printed by William Whiston he assured the reader that 'you will find in this little book certain particularities that you will seek in vain in great tomes on analysis.' His close associate Johann Bernoulli despite some adverse remarks paid Newton the compliment in 1728 of basing his own course on the elements of algebra upon Newton's text. Perhaps partly in consequence of Newton's recent death in Britain too the book began about this time to arouse greater interest than when it was first issued in 1707" Hall p. 174. Despite the impressive contributions of the work to the theory of equations mentioned earlier it is difficult to pigeonhole the work as being either algebraic or geometric. From one point of view the Arithmetica can be seen as a fulfillment of the programme outlined by Descartes in the Géométrie because it teaches how geometrical problems and also arithmetical and mechanical ones can be translated into the language of algebra. Paradoxically however Newton criticized Descartes maintaining that at least in some cases Apollonian geometry is to be preferred to Cartesian algebra in the analysis of indeterminate problems. Modern analysts he complained had confused algebra and geometry: "The Ancients so assiduously distinguished them one from the other that they never introduced arithmetical terms into geometry. recent people by confusing both have lost the simplicity in which all elegance in geometry consists" Papers V p. 429. The last section of the work 'The linear construction of equations' pp. 279-326 is particularly anti-Cartesian the term 'linear' in this context does not refer to straight lines but derives from Pappus. Newton here deals with the problem of constructing cubics third-degree equations that Descartes solved via the intersection of a circle and a parabola. Newton proposed instead to use a curve of degree higher than the conics as a means of construction namely the conchoid a fourth-degree curve. Newton regarded the conchoid as preferable because it has a mechanical construction and leads to a more elegant solution of the problem. The present 1722 revision is "the standard text of the Arithmetica published much as before 'Impensis Benj. & Sam. Tooke'. It appeared to Newton's first editor that 'that acute Mathematician Mr. John Machin Professor of Astronomy at Gresham College . and one of the Secretaries of the Royal Society published this Work again by the Author's later Desire or Permission; I lay no claim to it' Whiston Memoirs; John Conduitt's memorandum King's College Cambridge. Keynes MS 130.5 again adds the clarification that 'Machin overlooked the press for which Sir I intended to have given him 100 Guineas but he made him wait 3 years for a preface & then did not write one'. Elsewhere Keynes MS 130.6 2 Conduitt noted that 'Sir I. told me that Machin understood his Principia better than anybody that Halley was the best Astronomer but Machin the best Geometer'. Newton's active stage-managing of the 1722 revise can be documented in several ways: most notably a stray autograph sentence on an otherwise clean folio page now ULC. Add. 3960.7: 95 differs by only a single trivial adverb from an inserted footnote clarifying the reference to the unimplemented 'Regulae post docendae' on page 52 of the deposited copy. The ubiquitous presence of its author's editorial hand was not missed by W. J. 's Gravesande when he came to reissue the Arithmetica ten years later: 'Secunda vice liber in lucem prodiit Londini 1722; sed in statu perfectiore ut quis facile percipiat non omnino foetum abdicasse virum Celeberrimum; ordo propositionum non tantum mutatus est sed in ipsis solutionibus & demonstrationibus correctiones multae reperiuntur non nisi ipsi Auctori tribuendae'" ibid. p. 14 n 60. "Benjamin Tooke the London publisher and printer he was Queen's printer had eight books published at the Cambridge Press all of them by Whiston between 1702 and 1712. There are two London printer's ornaments used in this volume pp. 283 & 289 and nowhere else but we know that the woodcuts for the illustrations in the 1707 edition were delivered to Cambridge possibly from London 6d. was paid for the parcel. So far as one can tell the woodcuts are identical and we must assume they had been reclaimed by Tooke. Unfortunately we have no letters from Newton about the printing history of this volume" Macclesfield sale catalogue. Babson 200; Macclesfield 1520; Wallis 278. Gjertsen Newton Handbook 1986. Hall Isaac Newton 1992. Westfall Never at Rest 1983. 8vo pp. iv 332 including half-title with list of books on verso woodcut diagrams throughout ink name of Newton on half-title ink inscription identifying Newton as author and another Whiston as editor on title slightly browned. Contemporary panelled calf ink signature of former owner Robert Andrews on front free endpaper corners and edges rubbed joints splitting spine rubbed. Benji & Sam. Tooke unknown

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NEWTON, Sir IsaacBiblio.com

Arithmetica Universalis; sive de Compositione et Resolutione Arithmetica Liber. Ciu accessit Helleiana Aequationum Radices Arithmetice Inveniendi Methodus .

17074639Cambridge; London: Typis Academicus; Benjamin Tooke 1707. First edition. First edition of Newton's treatise on algebra or 'universal arithmetic' his "most often read and republished mathematical work" Whiteside. Included are 'Newton's identities' providing expressions for the sums of the powers of the roots of any polynomial equation plus a rule providing an upper bound for the positive roots of a polynomial and a generalization to imaginary roots of René Descartes' 'Rule of Signs.'. Hardcover. NEWTON'S TREATISE ON ALGEBRA. First edition of Newton's treatise on algebra or 'universal arithmetic' his "most often read and republished mathematical work" Whiteside. "Included are 'Newton's identities' providing expressions for the sums of the ith powers of the roots of any polynomial equation for any integer i pp. 251-2 plus a rule providing an upper bound for the positive roots of a polynomial and a generalization to imaginary roots of René Descartes' Rule of Signs pp. 242-5" Parkinson p. 138. About this last rule for determining the number of imaginary roots of a polynomial which Newton offered without proof Gjertsen p. 35 notes: "Some idea of its originality . can be gathered from the fact that it was not until 1865 that the rule was derived in a rigorous manner by James Sylvester." Provenance: Jesuit College at Ghent ink inscription 'Bibliotheca Collegii Gandavensis Societatis Jesu.' and shelfmark on title; extensive marginal annotations by a well-informed contemporary reader. This reader was possibly the English Jesuit Christopher Maier 1697-1767. Born in Durham England Maier entered the Society of Jesus in 1715. He taught at Liège where he became interested in astronomy. In 1750 Maire was commissioned by Pope Benedict XIV to measure two degrees of the meridian from Rome to Rimini with fellow Jesuit Roger Boscovich with a view to mapping the Papal States; in turn they proved that the earth is an oblate spheroid as Newton had proposed in Principia publishing their results in Litteraria Expeditione 1755. Maier spent his final years at the English Jesuit College in Ghent. "In fulfillment of his obligations as Lucasian Professor Newton first lectured on algebra in 1672 and seems to have continued until 1683. Although the manuscript of the lectures in Cambridge University Library carries marginal dates from October 1673 to 1683 it should not be assumed that the lectures were ever delivered. There are no contemporary accounts of them and apart from Cotes who made a transcript of them in 1702 they seem to have been totally ignored. Whiteside Papers V p. 5 believes that they were composed 'over a period of but a few months' during the winter of 1683-4" Gjertsen pp. 33-4. The course of lectures stemmed from a project on which Newton had embarked in the autumn of 1669 thanks to the enthusiasm of John Collins: the revision of Mercator's Latin translation of Gerard Kinckhuysen's Dutch textbook on algebra Algebra ofte stel-konst 1661. Newton composed a manuscript 'Observations on Kinckhuysen' in 1670 see Whiteside Papers II and used it in the preparation of his lectures. He took the opportunity not only to extend Cartesian algebraic methods but also to restore the geometrical analysis of the ancients giving his lectures on algebra a strongly geometric flavor. "When Newton resigned his Lucasian professorship to his deputy William Whiston in December 1701 it was natural that the latter should wish to familiarize himself with the deposited lectures of his predecessor" Whiteside Papers V p. 8. Whiston later claimed in his Memoirs London: 1749 that Newton gave him his reluctant permission to publish the lectures. Whiston arranged with the London stationer to underwrite the expense of printing the deposited manuscript and then subsequently between September 1705 and the following June corrected both specimen and proof sheets as they emerged from the University Press. The completed editio princeps finally appeared in May 1707 priced at 4s. 6d. without Newton's name on the title page although references inside the work made no attempt to hide the author's identity. It included an appended tract by Halley on 'A new accurate and easy method for finding the roots of any equations generally without prior reduction' pp. 327-343. Publication of the work had been delayed by Newton who complained that the titles and headings were not his and that it contained numerous mistakes. Yet when he prepared a second edition in 1722 the changes he introduced were "primarily reorderings of his own manuscript not corrections of Whiston's additions" Westfall p. 649. In reality Newton's misgivings probably derived more from his reluctance to place before the public a relatively immature and poorly organized work and one that did not take into account the developments in the subject that had taken place in the quarter century since the manuscript was composed. For a book that was to become Newton's most often republished mathematical work the Arithmetica initially made little impact in Britain and was not even graced by a review in the Philosophical Transactions. On the Continent the reception accorded the lectures was more positive. "Leibniz unhesitatingly divining their author beneath the cloak of anonymity gave them a long review in the Acta Eruditorum of Leipzig in 1708. Written thirty years before he noted and now deservingly printed by William Whiston he assured the reader that 'you will find in this little book certain particularities that you will seek in vain in great tomes on analysis.' His close associate Johann Bernoulli despite some adverse remarks paid Newton the compliment in 1728 of basing his own course on the elements of algebra upon Newton's text. Perhaps partly in consequence of Newton's recent death in Britain too the book began about this time to arouse greater interest than when it was first issued in 1707" Hall p. 174. Despite the impressive contributions of the work to the theory of equations mentioned earlier it is difficult to pigeonhole the work as being either algebraic or geometric. From one point of view the Arithmetica can be seen as a fulfillment of the programme outlined by Descartes in the Géométrie because it teaches how geometrical problems and also arithmetical and mechanical ones can be translated into the language of algebra. Paradoxically however Newton criticized Descartes maintaining that at least in some cases Apollonian geometry is to be preferred to Cartesian algebra in the analysis of indeterminate problems. Modern analysts he complained had confused algebra and geometry: "The Ancients so assiduously distinguished them one from the other that they never introduced arithmetical terms into geometry. recent people by confusing both have lost the simplicity in which all elegance in geometry consists" Whiteside Papers V p. 429. The last section of the work 'The linear construction of equations' pp. 279-326 is particularly anti-Cartesian the term 'linear' in this context does not refer to straight lines but derives from Pappus. Newton here deals with the problem of constructing cubics third-degree equations that Descartes solved via the intersection of a circle and a parabola. Newton proposed instead to use a curve of degree higher than the conics as a means of construction namely the conchoid a fourth-degree curve. Newton regarded the conchoid as preferable because it has a mechanical construction and leads to a more elegant solution of the problem. William Whiston 1667-1752 was "a member of the first generation of Cambridge students to emulate Newton's method and principles. He went up to Cambridge in 1686 claimed to have attended one or two incomprehensible lectures by Newton on his Principia and was elected a Fellow of Clare Hall in 1691. After taking orders he left Cambridge for a while returning in 1700 when chosen by Newton to be his deputy as Lucasian Professor. About a year later upon Newton's resignation and commendation Whiston succeeded him. Aberrant theology was to be his downfall. While Newton and their common friend Dr Samuel Clarke kept private their doubts about Trinitarianism the Creed and the Thirty-nine Articles Whiston sought publicly to amend the errors of the Anglican faith; for this he was summoned before the heads of houses in the university and dismissed from his post in 1710" Hall p. 175. Babson 199; Wallis 277; D. Gjertsen Newton Handbook 1986; A. R. Hall Isaac Newton 1992; R. S. Westfall Never at Rest 1983. 8vo pp. viii 343. Woodcut diagrams throughout. Former owner's signature F. Percy White Feb. 1920 on half-title partially erased. Contemporary mottled calf covers with floral border and corner fleurons in blind. / Hardcover. Typis Academicus; Benjamin Tooke unknown

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NEWTON, Sir IsaacBiblio.com

De mundi systemate liber

17286610London: J. Tonson J. Osborn & T. Longman 1728. First edition. First edition an extraordinary Newtonian association copy of Newton's rarest book inscribed by James Stirling recording the gift from Abraham de Moivre "Ja: Stirling Ex Dono Dni De Moivre". Drafted in the mid-1680s as the liber secundus of the earliest Principia the text differs substantially from the published Book III. Among its non-Principia contents are the thought-experiment of the orbiting cannonball anticipating the artificial satellite the first acceptable photometric determination of a stellar distance and passages that point to terrestrial tides Michelson 1919 and to the existence of the planet Uranus Herschel 1781. OCLC lists six copies worldwide; no copy in Cambridge.. An Exceptional Newtonian Association Copy. 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 bn 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 £50400 his own annotated copy of Principia £42840 and the Edinburgh silver pocket microscope by John Clark used in his Leadhills assays a further £42840: 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. References: Babson 16 - Wallis 19 - Norman 1593 English translation only - Gray 19 1731 reprint only - Cohen I. B. introduction to A Treatise of the System of the World London & Berkeley 1969 - Gjertsen D. The Newton Handbook London 1986 p. 573 - North J. D. Cosmos: An Illustrated History of Astronomy and Cosmology Chicago 2008 p. 418 - Tweddle I. James Stirling's Methodus Differentialis: An Annotated Translation of Stirling's Text London 2003 - Hoskin M. A. 'Newton Providence and the Universe of Stars' Journal for the History of Astronomy 8 1977 pp. 77-101 - Walker H. M. Studies in the History of Statistical Method Baltimore 1929 - The Library of James Stirling Mathematician Lyon & Turnbull Edinburgh 23 October 2025 lot 9. 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. . J. Tonson, J. Osborn & T. Longman unknown

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Elémens (éléments) de la philosophie de Neuton (Newton), donnés par Mr. de Voltaire. Nouvelle édition

Elémens (élèments) de la philosophie de Neuton (Newton), donnés par Mr. de Voltaire. Nouvelle édition

The Works of James Thomson. Volume The First only of Two. Containing The Seasons Liberty The Castle of Indolence and Poems on Several Occasions Includes also: "Antient and Modern Italy compared: Being the First Part of 'Liberty' A Poem".

Dissertations On The PropheciesWhich Have Remarkably Been Fulfilled And At This Time Are Fulfilling In The World. In Two Volumes. Volume The First.

Dissertations on the Prophecies volume II

Dissertations on the Prophecies Which have been remarkably fulfilled and at this time are fulfilling in the World in two volumes

Newton on the Prophesies. Volumes 2 and 3.

On the imperfect Reception of the Gospel. A Sermon Preached before the Incorporated Soceity for the Propagation of the Gopel in Foreign Parts; At Their Anniversary Meeting in the Parish Church of St. Mary-Le-Bow on Friday February 17 1769

Bildnis Sir Isaac Newton. Schabkunstblatt nach Sir Godfrey Kneller (1646 Lübeck - 1723 London)

Philosophiae Naturalis Principia Mathematica

errae-Filius; or the Secret History of the University of Oxford; in several essays. To which are added Remarks upon the late book entitled University Education by R. Newton Vol 1

Geschichte und gegenwärtiger Zustand der Optik, vorzüglich in Absicht auf den physikalischen Theil dieser Wissenschaft. Aus dem Englischen übersetzet und mit Anmerkungen und Zusätzen begleitet von Georg Simon Klügel.

Opuscula Mathematica Philosophica et Philologica: Collegit partimque Latine vertit ac recensuit Joh. Castilloneus Jurisconsultus 3 Volumes Complete

An Account of Sir Isaac Newton’s Philosophical Discoveries in Four Books. Published from the Author’s Manuscript Papers by Patrick Murdoch.

The History and Antiquities of Maidstone the County-Town of Kent. From the Manuscript Collections of William Newton Minister of Wingham in the said County .

Afhandlinger over Prophetierne hvilke merkværdig ere opfyldte og paa denne Tid blive opfyldte i Verden. Oversat af Diderik de Thurah. 3 Bd.

Dissertations on the Prophecies Which Have Remarkably Been Fulfilled and at This Time Are Fulfilling in the World: Volumes One and Two

Dissertations on the Prophecies Which Have Remarkably Been Fulfilled and at This Time are Fulfilling in the World - Volume II

Arithmetica Universalis; sive de Compositione et Resolutione Arithmetica Liber. Ciu accessit Helleiana Aequationum Radices Arithmetice Inveniendi Methodus .

Arithmetica Universalis; sive de Compositione et Resolutione Arithmetica Liber. Ciu accessit Helleiana Aequationum Radices Arithmetice Inveniendi Methodus .

De mundi systemate liber

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