https://www.amazon.co.uk/New-Compendium-Whole-Practical-Navigation/dp/1173621032/?tag=prabook0b-20
1702
https://www.amazon.co.uk/Synopsis-Palmariorum-Matheseos-William-Jones/dp/1174944803/?tag=prabook0b-20
1706
educator mathematician scientist author
William Jones was born c. 1675 in Llanfihangel Tre'r Beirdd, Isle of Anglesey, Wales (the next farm to the birthplace of Lewis, Richard, and William Morris). He was the son of a poor farmer, John George Jones, and of Elizabeth Rowland. The family moved to Tyddyn-bach, Llanbabo, and when the father died the mother went to live at Clymwr in the same parish.
Jones attended a charity school at Llanfechell, also on the Isle of Anglesey, where his mathematical talents were spotted by the local landowner who arranged for him to be given a job in London working in a merchant's counting-house.
Jones traveled to the West Indies and taught mathematics on a man-of-war. Upon his return to London, Jones established himself as a teacher of mathematics; tutorships in great families followed. One of his pupils, Philip Yorke (afterward first earl of Hardwicke), later became lord chancellor; Jones traveled with him on circuit and was appointed "secretary for peace." He also taught Thomas Parker, afterwards the first earl of Macclesfield, and his son George, who became president of the Royal Society.
In 1702 Jones published A New Compendium of the Whole Art of Navigation, a practical treatise concerned with the application of mathematics to astronomy and seamanship. His second book, Synopsis palmariorum matheseos (1706), attracted the attention of Newton and Halley. The book was designed essentially for beginners in mathematics, but it contained a fairly comprehensive survey of contemporary developments, including the method of fluxions and the doctrine of series. Although all the symbols used by Jones are sensible and concise, in only one respect does he appear to have been an innovator: he introduced π for the ratio of the circumference of a circle to the diameter.
From 1706 on, Jones remained in close touch with Newton and was one of the privileged few who obtained access to his manuscripts. About 1708 he acquired the papers and correspondence of John Collins, a collection that included a transcript of Newton’s De analysi (1669). In 1711 Newton permitted Jones to print the tracts De analysi per aequationes numero terminorum infinitas and Methodus differentialis (along with reproductions of his tracts on quadratures and cubics) as Analysis per quantitatum series, fluxiones ac differentias; cum enumeratione linearum tertii ordinis. In the same year, Jones was appointed a member of the committee set up by the Royal Society to investigate the invention of the calculus. With John Machin and Halley, he was responsible for the preparation of the printed report. He also contributed sundry papers to the Philosophical Transactions, mostly of a practical character.
At his death Jones left a voluminous collection of manuscripts and correspondence which he had assembled mainly through his connections with Newton and the Royal Society. It seems that he intended to publish an extensive work on mathematics and, to this end, made copious notes and transcripts from manuscripts lent by Newton. This material became inextricably mixed with the original manuscripts and the transcripts of others, including those of John Collins and James Wilson. John Coulson (1736) used a transcript made by Jones as the basis for an English version of Newton’s 1671 tract, The Method of Fluxions and Infinite Series. Subsequently, Samuel Horsley retained Jones’s title for the tract on fluxions (1671) and copied the “dot” notation inserted by Jones. D. T. Whiteside remarks that the sections of the Portsmouth collection relating to fluxions are “choked with irrelevant, fragmentary transcripts by Jones and Wilson.”
After Jones' death most of the manuscript collection passed into the hands of the second earl of Macclesfield. Two volumes of correspondence from this collection were published by Rigaud in 1841. The task of separating the mass of material compiled by Jones from Newton’s original manuscripts has only recently been completed by Whiteside.
William Jones went down in history as a distinguished self-taught mathematician who introduced the concept of Pi to represent the ratio of the circumference of a circle to its diameter; this became one of the mathematical constants. He is also known for his works A New Compendium of the Whole Art of Navigation and Synopsis palmariorum matheseos, which concerned the application of mathematics to astronomy and seamanship and included theorems on differential calculus and infinite series.
Jones believed that π was an irrational number: an infinite, non-repeating sequence of digits that could never totally be expressed in numerical form. Consequently, a symbol was required to represent an ideal that can be approached but never reached. For this Jones recognized that only a pure platonic symbol would suffice.
On November 30, 1712, Jones was elected a fellow of the Royal Society and subsequently became vice-president.
Jones married twice, firstly the widow of his counting-house employer, whose property he inherited on her death; and secondly, in 1731, Mary, the 22-year-old daughter of cabinet-maker George Nix. The couple had two surviving children.
William Jones was a renowned philologist who established links between Latin, Greek and Sanskrit, leading to the concept of the Indo-European language group.
