Oughtred, William

(bap. 1575, d. 1660), mathematician

by Frances Willmoth

© Oxford University Press 2004 All rights reserved

Oughtred, William (bap. 1575, d. 1660), mathematician, was the son of Benjamin Oughtred (d. 1618), a writing-master and 'registrar' at Eton College, and was baptized there on 5 March 1575 (reputedly the day of his birth). After attending the school as a king's scholar and being taught arithmetic by his father, he went on to King's College, Cambridge, in 1592; he became a fellow there in 1595, graduating BA in 1596 and proceeding MA in 1600. He later said that it was during this period that he began to study mathematics intensively, and 'by inciting, assisting and instructing others, brought many in to the love and study of those Arts, not only in our own, but in some other Colledges also' (Oughtred, sig. [A4]v). His first known mathematical writings and instrument designs date from this period, although they appeared in print much later.

Having been ordained priest in 1603, Oughtred left the university in 1605 to become vicar of Shalford, in Surrey; he was rector of nearby Albury from 1610 until his death. The move to Shalford enabled him to marry Christsgift Caryll, baptized at Godalming, Surrey, on 21 April 1588, as a daughter of William Caryll or Carell and his wife, Doryty. The Carylls lived at Tangley in the parish of Wonersh (not far from Shalford), and Christsgift's marriage to Oughtred took place there on 20 February 1606. Oughtred also built up links with other local families, teaching mathematics to the son of Sir Francis Aungier and Latin to a member of the household of George Duncombe. This did not mean that his horizons narrowed; he mentions having met Edmund Gunter through the good offices of 'my honoured friend, Master Henry Briggs', while on a visit to London in 1618. About 1620 Oughtred first encountered one Captain Marmaduke Neilson or Nelson, who proposed an astronomical method of finding longitude at sea; Neilson seemed to admit that he was wrong, but was to reappear in the early 1630s making similar claims, with the backing of Lord Falkland. Oughtred was then consulted about the matter by Peter Heylin, and appointed to a commission consisting of several learned men set up to reconsider it in May 1636.

Meanwhile Oughtred was introduced to Thomas Howard, second earl of Arundel (1586-1646), as he described in 1633:

About five yeares since, the Earle of Arundell my most honourable Lord in a time of his private retiring to his house ... at West Horsley, foure small miles from me ... hearing of me ... was pleased to send for me: and afterward at London to appoint mee a chamber in his owne house [Arundel House, in the Strand]. (Oughtred, sig. Bv)
There are hints that Oughtred hoped for more concrete benefits from the relationship, perhaps in terms of church preferments, but he was disappointed. His sole acquisition was the Heathfield prebend at Chichester Cathedral, bestowed upon him by Bishop Henry King, who lived in Surrey during the civil war period and was a cousin of George Duncombe; King allowed his son John to become one of Oughtred's pupils. The grant was made in or after 1644, so can only have been a purely nominal honour; it may have been intended as a compensation for Oughtred following his complaint, in 1647, that John King had seduced one of his daughters (Crum, 20).

In return for the earl's patronage Oughtred taught his second surviving son, William (later Viscount Stafford). It was for this pupil, he said, that he compiled his Arithmeticae in numeris et speciebus institutio: quae ... totius mathematicae quasi clavis est (1631). In this he took algebraic methods from continental sources, especially Viète, and presented them in a concise form through the intensive use of symbols, some of which were invented by himself; the resulting volume was relatively small and inexpensive, in marked contrast to the rival work of Thomas Harriot (posthumous, also 1631). In presenting a copy to Peter Heylin, Oughtred described it as:

but a mole-hyll, easily stept over. Some thinke it hard; it is indeed new to this our age; but either this, or els some such like, familiar to the ancients ... and indeed analytice is the true way of invention ... it is not hard: it is the way of nature, which is most plaine and easie, and free from anfractuous ambiguities, in all her workes. (Bodl. Oxf., MS Rawl. D.353, fol. 96)
An English edition of the Clavis, translated by Dr Robert Wood, appeared in 1647 as The Key of the Mathematics New Forged and Filed, with a preface in which Oughtred thanked Thomas Wharton, Jonas Moore, and others for helping to see the volume through the press. A number of his shorter mathematical writings were appended to the second and third Latin editions, which appeared under the title Clavis mathematica(e) in 1648 and 1652 respectively. The latter of these was produced in Oxford by a group including John Wallis (1616-1703), Seth Ward (1617-1689), and the young Christopher Wren (1632-1723). It reflects the unique status Oughtred had by then attained as a figurehead for contemporary English mathematicians.

Oughtred's position in the Howard household allowed him to make contact with other members of the mathematical community in London, including various instrument makers. He had a close relationship with Elias Allen, whose workshop by St Clement Danes was only a short distance down the Strand from Arundel House, and he was later in contact with Allen's apprentice and successor Ralph Greatorex. Allen was responsible for realizing various instrument designs for Oughtred--some devised during his time in Cambridge and some soon after his first encounter with logarithms. The latter instruments included the 'circles of proportion'--the earliest form of slide-rule--which allowed problems of multiplication and division to be reduced to addition and subtraction by the use of logarithms. Oughtred was persuaded by one of his pupils, William Forster, to publish an account of this device, despite his consistent wariness about promoting the use of instruments. He believed that their availability often kept people from studying the theoretical aspects of mathematics. The Circles of Proportion and the Horizontal Instrument ... Invented, and the Uses of Both Written in Latine by Mr W.O., Forster's translation, was published in 1632. The second instrument of the title, placed on the back of the circles of proportion, was a tool for demonstrating astronomical principles and for laying out sundials on any kind of plane. It was later adapted to make a garden sundial, of which Oughtred published an account in The Description and Use of the Double Horizontall Dyall (1636). The circles of proportion and especially the horizontal instrument involved Oughtred (and Forster) in a bitter dispute with Oughtred's former pupil Richard Delamain, who had also published accounts of both instruments as his own invention. Oughtred retaliated in a piece usually found bound with The Circles of Proportion: To the English gentrie ... the just apologie of Wil: Oughtred, against the slaunderous insimulations of Richard Delamain [1633]. In this he made a scathing attack on those mathematical teachers who were more interested in the use of instruments than the study of mathematical theory, calling them 'doers of tricks' and 'Jugglers'. Here and elsewhere he defended the unity of mathematics, deploring the 'superficiall scumme and froth of Instrumentall tricks and practices' that emerged when practice was not based upon sound theoretical understanding.

Other instruments Oughtred developed included a straight slide-rule (described in the preface to The Circles of Proportion and in a letter to Elias Allen), a gauging rod (described in The New Artificial Gauging Line, 1633), and another sundial, which was to become one of the most popular of its type in the seventeenth and eighteenth centuries. This last instrument had already been available from Allen's workshop for about twenty years when an account of it was published in 'The description of the generall horologicall ring', appended to a new edition of The Description and Use of the Double Horizontall Dyall (1652).

Forster was one of the many men who went to Oughtred in London or at Albury to benefit from his tuition and from access to his unparalleled mathematical library. The list of his disciples includes many eminent contemporary mathematicians and scholars--Seth Ward, Christopher Wren, Laurence Rooke, and Jonas Moore being only the best known of them--though it is now difficult to be sure which were genuinely his pupils and which were simply admiring colleagues. Many of them made use of the Clavis as a teaching text: Ward is said to have employed the work in his university teaching at Cambridge in the early 1640s, and Rooke to have lectured upon it at Gresham College in the 1650s. The Savilian professor John Wallis also paid homage to Oughtred and produced another edition of the Clavis in 1667.

Other works by Oughtred are The Solution of All Sphaerical Triangles by the Planisphere (1651, ed. Christopher Brookes); Trigonometria (1657, Englished by Richard Stokes as Trigonometrie); and the posthumous Opuscula mathematica (1677) containing various previously unpublished short treatises. He is also credited, probably incorrectly, with an English translation (in 1633) of Jean Leurechon's Recreations mathematiques of 1629. The 'planisphere' mentioned in the first of these works was yet another of Oughtred's inventions, devised about 1610 along with an instrument 'giving the Prosthaphaereses of the Plannets according to the Theory of Copernicus' (W. Oughtred, The Solution of All Sphaerical Triangles by the Planisphere). Both instruments had astrological uses. Oughtred's interest in astronomy was inseparably bound up with belief in astrology; Aubrey reports that he was also deeply committed to the study of alchemy. The impression his neighbours gained of these activities may have reinforced the threat to his tenure of the Albury living when, in 1646, he was brought before a sequestration committee for his loyalty to the royalist cause. The parliamentarian astrologer William Lilly claimed credit for organizing his defence; Aubrey believed that the Surrey landowner Sir Richard Onslow was primarily responsible for its successful outcome and that this was why the 1647 Key of the Mathematics was dedicated to Onslow and his son.

Oughtred and his wife had thirteen children, according to Aubrey, or twelve according to a note of names and dates preserved by Ashmole: William, Henry (twice), Benjamin, Simon, Margaret, Judith, Edward, Elizabeth, Anne, George, and John. Benjamin and John became watchmakers. The family connection with the instrument-making trade was further strengthened by the marriage of one of the daughters to Christopher Brookes, an apprentice of Elias Allen and the editor of Oughtred's treatise on spherical triangles. Oughtred died on 13 June 1660, probably at Albury, where he was buried on 15 June; Aubrey writes that he expired with joy on hearing of the king's restoration. The administration of his estate was granted to his son, Henry, on 24 July 1661. While some of his books were dispersed, others, with some of his papers, eventually reached the hands of the mathematician William Jones: the books were merged with other contents of a private library during the nineteenth century, and cannot now be separately identified.


F. H. Willmoth, Sir Jonas Moore: practical mathematics and Restoration science (1993), chap. 2
H. K. Higton, 'Elias Allen and the role of instruments in shaping the mathematical culture of seventeenth-century England', PhD diss., U. Cam., 1996
Brief lives, chiefly of contemporaries, set down by John Aubrey, between the years 1669 and 1696, ed. A. Clark, 2 (1898), 105-15
A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali dell' Istituto e Museo di Storia della Scienza di Firenze, 6 (1981), 99-201
W. Oughtred, To the English gentrie ... the just apologie of Wil: Oughtred against the slaunderous insimulations of Richard Delamain [1633]
notes about Oughtred, Bodl. Oxf., MS Ashmole 1137, fol. 3v
H. C. Malden, ed., The parish registers of Godalming, pt 1 (1904), 9
W. Sterry, ed., The Eton College register, 1441-1698 (1943), 253
G. L. Hennessy, Chichester diocese clergy lists (1900), 9
D. Lloyd, Memoires of the lives ... of those ... personages that suffered ... for the protestant religion (1668), 608
W. Kennett, A register and chronicle ecclesiastical and civil (1728), 721
CSP dom., 1635-6
G. Vernon, The life of the learned and reverend Dr Peter Heylin (1628), 43-9
will, PRO, PROB 6/37, fol. 61
The poems of Henry King, bishop of Chichester, ed. M. Crum (1965), 20
private information (2004)
parish register (marriage), Wonersh, 20 Feb 1606

NRA, priv. coll., books and papers

W. Hollar, etching, 1644, BM; repro. in W. Oughtred, Clavis mathematicae, 2nd edn (1648), frontispiece
G. P. Harding, watercolour drawing (after W. Hollar), NPG
W. Hollar, drawing, BM [see illus.]

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