Newton Papers : Fluxions

Newton, Isaac, Sir, 1642-1727

Newton Papers

<p style='text-align: justify;'>The items in Add. 3960 were composed in different periods, from the mid 1660s [<a href='' onclick='store.loadPage();return false;'>Add. 3960.12</a>] to the early 1690s and early 1700s, when Newton planned to write a treatise on the calculus, what he termed ‘the methods of series and fluxions’. </p><p style='text-align: justify;'>The first three items are not in Newton’s hand and are interesting since they document the use and diffusion of copies of Newton’s manuscripts in the early decades of the eighteenth century. In part, this dissemination was promoted by William Jones, the librarian and mathematics tutor of the Earl of Macclesfield. An avid book and manuscript collector, Jones was admitted to Newton’s close entourage. In 1711 he was appointed to the Royal Society committee set up to arbitrate the dispute between Newton and Leibniz (on which see <a href='/view/MS-ADD-03968'>Add. 3968</a>). Thanks to his acquisition of the papers of John Collins and the close association with Newton during the dispute, Jones was able to collect and transcribe many of Newton’s mathematical papers.</p><p style='text-align: justify;'>The first item [<a href='' onclick='store.loadPage(3);return false;'>3960.1</a>], found among Mr Raper’s Papers, is probably in James Wilson’s hand (this hand can be found also in <a href='' onclick='store.loadPage(91);return false;'>Add. 3960.3, pages 1-28</a>). It consists of secondary transcripts from some of Newton’s early works on fluxions, including the so-called ‘October 1666 Tract on Fluxions’ <a href='/view/'>Add. 3958, fols 48v-63v</a>. One can find also notes on Leibniz’s papers published in the Leipzig journal <i>Acta Eruditorum</i> [<a href='' onclick='store.loadPage(50);return false;'>page 48</a>] and notes ‘Extracted from the papers Mr Jones gave to one Mr Watkins a Scholar of his’ [<a href='' onclick='store.loadPage(52);return false;'>page 50</a>]. It is interesting to note that Newton’s original papers of the 1660s are transcribed with some alterations. The notation employed is the characteristic dotted notation (which Newton invented only in the early 1690s). There are terminological variants too: in this transcripton the term ‘fluxion’ is interpolated as equivalent to the original ‘velocity’ and several passages are massaged in order to make them more rigorous [<a href='' onclick='store.loadPage(3);return false;'>page 1 and following]</a>. All this must have occurred in the context of the priority dispute on the invention of the calculus that Newton had with Gottfried Wilhelm Leibniz in the 1710s.</p><p style='text-align: justify;'>When, in the early 1730s, Thomas Birch began planning a biography of Newton, which he published in <i>A General Dictionary, Historical and Critical</i> (London, 1738), VII, pp. 776-802, he must have consulted the tract on the history of fluxions that can be found here [<a href='' onclick='store.loadPage(67);return false;'>Add. 3960.2</a>]. In this hagiographic reconstruction of Newton’s early discoveries of the calculus, use is made of the Waste Book [<a href='/view/MS-ADD-04004/117'>Add. 4004: 57r-57v</a>], of the ‘October 1666 Tract on Fluxions’ [<a href='/view/MS-ADD-03958/92'>Add. 3958, fols 48v-63v</a>], and other early writings by Newton. Birch was not the last to use this tract. David Brewster, the main nineteenth-century biographer of Newton, saw it: his annotation can be seen in the margin of the first page [<a href='' onclick='store.loadPage(67);return false;'>3960.2, page 1</a>]. </p><p style='text-align: justify;'>Add. 3960 bears other traces of rare uses of the Portsmouth Collection before the acquisition of these papers in 1872. Indeed, Samuel Horsley, the editor of Newton’s <i>Opera quae exstant omnia, </i>5 vols (London: J. Nichols, 1779-1785), in 22 October 1777 notes that a paper in which Newton attempts a geometric rigorous foundation for the rules of the method of fluxions [<a href='' onclick='store.loadPage();return false;'>3960.5, front-cover, image 139</a>] is ‘very proper to be published’.</p><p style='text-align: justify;'>Many items in Add. 3960 relate to Newton’ planning, drafts, publication, and revision of <i>Tractatus de quadratura curvarum</i>, a treatise devoted to what we would now call integration, which Newton composed in the early 1690s, reworked in the early 1700s, and eventually published as an appendix to the <i>Opticks</i> (1704). Other papers on quadratures can be found elsewhere in the Portsmouth and Macclesfield Collections, most notably in <a href='/view/MS-ADD-03962'>Add.3962</a>.</p><p style='text-align: justify;'>Undoubtedly, the mathematical gem in Add. 3960 is <a href='' onclick='store.loadPage();return false;'>Add. 3960.14</a> (see also the preliminary drafts in <a href='' onclick='store.loadPage(91);return false;'>Add. 3960.3, pages 29-32</a>). This is the so-called <i>De methodis serierum et fluxionum</i>, a title that must be inferred, with much uncertainty, from other sources such as the correspondence and from Newton’s own late recollections, since the first folio is missing. Newton began composing this lengthy treatise in 1670, worked on it for about one year, and possibly continued to add and interpolate material in subsequent periods (see, for example, Newton’s late statement ‘in tractatu quem anno 1671 conscripsi’ <a href='/view/MS-ADD-03968/91'>Add. 3968.6, fol. 46r</a>). Newton begins with a clear handwriting, placing well-crafted figures accurately, and adding annotations in the margin that seem addressed to a printer. Later in the text, the treatise decreases in tidiness. The <i>De methodis</i> is incomplete (<a href='' onclick='store.loadPage();return false;'>Add. 3960.4</a> was probably meant to be an addendum to it) and remained unpublished during Newton’s lifetime. The rather obscure Lucasian Professor John Colson published a commented English translation in 1736 (which was pirated in the subsequent year). Most likely, Colson used a transcription belonging to William Jones, now in the Macclesfield Collection [Add 9597.9.2]. The <i>Method of Fluxions</i> became one of Newton’s most widely read mathematical works. It was soon translated into French by Georges-Louis Leclerc de Buffon in 1740 and in 1744 back into Latin (from Colson’s English) by the Italian Calvinist refugee Giovanni Francesco Salvemini (Jean de Castillon or Castillioneus). The <i>Method of Fluxions</i>, now available in the two main languages of the Republic of Letters, could however be just admired: it was too late for it to exert any influence on cutting-edge research.</p><p style='text-align: justify;'>Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.</p>