William Oughtred ( AWT-urd;5 March 1574 – 30 June 1660), also Owtred or Uhtred, was an English mathematician and Anglican clergyman. After John Napier discovered logarithms and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, Oughtred was the first known to use two such scales in separate rods sliding by one another to perform direct multiplication and division. He is credited with being second inventing the slide rule instrument in about 1632. He also introduced the "×" symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions.
The son of Benjamin Oughtred of Eton in Buckinghamshire (now part of Berkshire), William was born there on 5 March 1574/75 and was educated at Eton College, where his father, a writing-master, was one of his teachers. Oughtred had a passion for mathematics, and often stayed awake at night to learn while others were sleeping. He next attended King's College, Cambridge, where he graduated BA in 1596/97 and MA in 1600, holding a fellowship in the college from 1595 to 1603. He composed a Funeral Ode in Latin for Sir William More of Loseley Park in 1600.
Rector at Guildford and at Shalford
Admitted to holy orders, he left the University of Cambridge about 1603, when as "Master" William Oughtred he held the rectorate of St Mary's Church, Guildford, Surrey. At the presentation of the lay patron George Austen, gent., he was instituted as vicar at Shalford near Wonersh, in the neighbourhood of Guildford in western Surrey, on 2 July 1605.
On 20 February 1606, at Shalford, Oughtred married Christs-gift Caryll, a relation of the Caryll family seated at Great Tangley Hall at Shalford. The Oughtreds had twelve children, William, Henry, Henry (the first Henry died as a baby), Benjamin, Simon, Margaret, Judith, Edward, Elizabeth, Anne, George, and John. Two of the sons, Benjamin and John, shared their father's interest in instruments and became watchmakers.
Oughtred's wife was a cousin of Simon Caryll of Tangley and his wife Lady Elizabeth Aungier (married 1607), daughter of Sir Francis Aungier. Oughtred was a witness to Simon Caryll's will, made 1618, and through two further marriages Elizabeth remained matriarch and dowager of Great Tangley until her death in about 1650. Elizabeth's brother Gerald, 2nd Baron Aungier of Longford, was married to Jane, daughter of Sir Edward Onslow of Knowle, Surrey, in 1638. Oughtred praised Gerald (whom he taught) as a man of great piety and learning, skilled in Latin, Greek, Hebrew and other oriental languages.
In January 1610 Sir George More, patron of Compton church adjacent to Loseley Park, granted the advowson (right of presentation of the minister) to Oughtred, when it should next fall vacant, though Oughtred was not thereby empowered to present himself to the living. This was soon after Sir George More became reconciled to the marriage of his daughter Anne to the poet John Donne, which had occurred secretly in 1601.
Oughtred was presented by Sir Edward Randyll of Chilworth (lord of the manor) to the rectory of Albury, near Guildford in Surrey and instituted on 16 October 1610, vacating Shalford on 18 January 1611.
In January 1615/16 Sir George More re-granted the advowson of Compton church (still occupied) in trust to Roger Heath and Simon Caryll, to present Oughtred himself, or any other person whom Oughtred should nominate, when the vacancy should arise. Soon afterwards Oughtred was approached by John Tichborne seeking his own nomination, and entering an agreement to pay him a sum of money upon certain days. Before this could be completed the incumbent died (November 1618), and Oughtred sought for himself to be presented, preaching several times at Compton, having the first fruits sequestered to his use, and, after four months, asking the patron to present him. However, Tichborne offered to complete the agreed payment at once, and was accordingly presented by the trustees in May 1619 (Simon Caryll dying in that year): but before he could be admitted, the Crown interposed a different candidate because the contract between Oughtred and Tichborne was deemed by Sir Henry Yelverton clearly to be Simoniacal.
Oughtred therefore remained at Albury, serving as rector there for fifty years. His patron, the Earl of Arundel, acquired the fine old seat of Albury House through trustees in 1638: title to the manor was assigned in trust for payment of debts to George Duncombe (of Weston in Albury, embedded in the Carrill and Onslow interests), who maintained the manorial courts until his death in 1646, and then to Duncombe's children. The Park and landscapes, which formed the subject of a series of etchings produced by Wenceslas Hollar, c. 1645, were developed in this period, before a parliamentary sequestration which was eventually discharged in 1653. The Earl having died in 1646, and his son and successor Henry (who renewed the assignment) in 1652, it was the grandson Henry Howard (later Duke of Norfolk) who finally paid for and acquired Albury.
William Lilly, that celebrated astrologer, knew Oughtred and claimed in his autobiography to have intervened on his behalf to prevent his ejection from his living by Parliament in 1646:"About this time, the most famous mathematician of all Europe, Mr. William Oughtred, parson of Aldbury in Surry, was in danger of sequestration by the Committee of or for plundered ministers; (Ambo-dexters they were;) several inconsiderable articles were deposed and sworn against him, material enough to have sequestered him, but that, upon his day of hearing, I applied myself to Sir Bolstrode Whitlock, and all my own old friends, who in such numbers appeared in his behalf, that though the chairman and many other Presbyterian members were stiff against him, yet he was cleared by the major number." Of his portrait (aged 73, 1646) engraved by Wenceslas Hollar, prefixed to the Clavis Mathematica, John Evelyn remarked that it "extreamly resembles him", and that it showed "that calm and placid Composure, which seemed to proceed from, and be the result of some happy ἕυρησις and Invention". William Oughtred died at Albury in 1660, a month after the restoration of Charles II. A staunch supporter of the royalty, he is said to have died of joy at the knowledge of the return of the King. He was buried in Old St Peter and St Paul's Church, Albury. Autobiographical information is contained in his address "To the English gentrie" in his Just Apologie of c. 1634.
Oughtred developed his interest in mathematics early in life, and devoted whatever spare time his academic studies allowed him to it. Among the short tracts added to the 1647/48 editions of the Clavis Mathematica was one describing a natural and easy way of delineating sun-dials upon any surface, however positioned, which the author states he invented in his 23rd year (1597/98), which is to say, during his fellowship at King's College, Cambridge. His early preoccupation was to find a portable instrument or dial by which to find the hour, he tried various contrivances, but never to his satisfaction. "At last, considering that all manner of questions concerning the first motions were performed most properly by the Globe itself, rectified to the present elevation by the help of a moveable Azimuth; he projected the Globe upon the plane of the Horizon, and applied to it at the center, which was therein the Zenith, an Index with projected degrees, for the moveable Azimuth."
This projection answered his search, but then he had to invent theorems, problems and methods to calculate sections and intersections of large circles, which he could not find by instruments, not having access to any of sufficient size. In this way he drew out his findings, presenting one example to Bishop Thomas Bilson (who had ordained him), and another, in about 1606, to a certain noble lady, for whom he wrote notes for its use. In London, in spring 1618, Oughtred visited his friend Henry Briggs at Gresham College, and was introduced to Edmund Gunter, Reader in Astronomy, then occupying Dr Brooks's rooms. He showed Gunter his "Horizontall Instrument", who questioned him closely about it and spoke very approvingly. Soon afterwards Gunter sent him a print taken from a brass instrument made by Elias Allen, after Oughtred's written instructions (which Allen preserved). When, in 1632, Richard Delamain the elder claimed that invention for himself, William Robinson wrote to Oughtred: "I cannot but wonder at the indiscretion of Rich. Delamain, who being conscious to himself that he is but the pickpurse of another man's wit, would thus inconsiderately provoke and awake a sleeping lion..."