Newton Papers : Elementary Mathematics

Newton, Isaac, Sir, 1642-1727

Newton Papers

The papers in Add. 3959 mostly relate to Newton’s activities as a mathematics teacher and an editor of mathematical books, enterprises that concerned him after his election to the Lucasian Chair in 1669. As Lucasian Professor, Newton was supposed to give a lecture every week during term, and to submit written versions of at least ten lectures per year for deposit in the University Library [for example Ms. Dd. 4.18; <a href='/view/MS-ADD-04002/1'>Add. 4002</a>]. It seems that as a teacher Newton did not have a large following, and it is unclear whether his lessons were actually attended by students. The legend, handed down by his aide and secretary Humphrey Newton, whereby Newton held his lectures in deserted classrooms, and ‘for want of Hearers, read to the Walls’ [MS Keynes 135, fol. 2 (King's College, Cambridge)], should not entirely be believed. Here, in fact, we have a set of lectures on trigonometry [<a href='' onclick='store.loadPage(47);return false;'>Add. 3959.4</a> and <a href='' onclick='store.loadPage(65);return false;'>Add. 3959.5</a>]. They are mostly a commentary on a lost manuscript treatise by St John Hare (probably the person of this name who matriculated at Christ Church, Oxford, in 1648 and was later a barrister; see also Add. 3997 and Add. 3998, two treatises by Hare which Newton owned). Hare’s trigonometry is based on Seth Ward’s introductory manual, Idea trigonometriae demonstratae (Oxford, 1654). Newton’s trigonometric writings, penned probably in the early 1680s, that can be found in Add. 3959 are sometimes in the hand of his amanuensis Humphrey Newton (no relation), and further exist in the form of a transcript (in which Newton’s lectures are firmly dated as ‘given in 1683’) written by a student, Henry Wharton – destined to become chaplain to the Archbishop of Canterbury, historian of the Church of England and the recipient of a funerary anthem by Henry Purcell [now Ms. 592 at Lambeth Palace Library]. According to his biographer, Wharton acquired ‘no mean skill in Mathematicks ... by the kindness of Mr. Isaac Newton … who was pleased to give him further instructions in that noble Science, amongst a select Company in his own private Chamber’ (Fourteen Sermons Preach’d in Lambeth Chapel … with and Account of the Author’s Life. The Second Edition Corrected (London, 1700): sig. A3v-A4r).Newton was the second Lucasian Professor. The first was Isaac Barrow. It was through Barrow’s intermediation, that in 1669 Newton got in touch with John Collins, an amateur mathematician who supplemented his modest living as a civil servant by entrepreneurial activities in the field of mathematical book publishing. This sector suffered in the depression in the print business caused by the Great Fire of London, but Collins managed to supervise the publication of several books, mostly related to algebra and navigation. In these disciplines there was a great need to update what was then available on the English market.For Newton, getting in touch with Collins meant achieving free access to a network of mathematical correspondents, both in Britain and on the continent, and to the bustling world of printers and booksellers active in the capital. In the early 1670s, Newton busied himself in the edition for the English market of a successful textbook on geography (Bernhardus Varenius, Geographia generalis (Amsterdam, 1650)), which was published by a Cambridge bookseller and printed by the University’s printer in 1672. In late 1669 and in 1670 Newton, again at Collins’s prompting, did a great deal of work to update the Latin translation of a Dutch treatise on algebra. The Dutch treatise is Algebra ofte stel-konst (Haarlem, 1661) by Gerard Kinckhuysen. Collins was in possession of a Latin translation by Nicolaus Mercator, a German mathematician who had moved to London. Mercator had translated the book at the request of William Brouncker, the first President of the Royal Society. Mercator’s manuscript, interleaved in the Dutch original, and annotated by Newton, is now extant in the Bodleian Library (Savile G. 20 (4)). In <a href='' onclick='store.loadPage(3);return false;'>fols 2r-21r</a> one finds Newton’s observations on and critique of Kinckhuysen’s text. These annotations developed into Newton’s Lucasian lectures on algebra [Ms. Dd.9.68] which Newton deposited in the University Library late 1683 or early 1684. These lectures were first printed thanks to the initiative of William Whiston, Newton’s successor in the Lucasian Chair, and appeared with the title Arithmetica universalis in 1707. In the eighteenth century this became Newton’s most widely read and republished book. Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.