William Oughtred
William Oughtred , also Owtred, Uhtred, etc., was an English mathematician and Anglican clergyman. After John Napier discovered logarithms and Edmund Gunter created the logarithmic scales upon which slide rules are based, Oughtred was the first to use two such scales sliding by one another to perform direct multiplication and division. He is credited with inventing the slide rule in about 1622. He also introduced the "×" symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions.
Clerical life
Education
The son of Benjamin Oughtred of Eton in Buckinghamshire, 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 would often stay awake at nights to learn while others were sleeping. He then 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, 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, 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 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 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.
Rector of Albury
Oughtred was presented by Sir Edward Randyll of Chilworth 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 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, 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 : 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, 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 in 1652, it was the grandson Henry Howard 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; 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 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.
Mathematician
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, 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, 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. 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..."
Around 1628 he was appointed by the Earl of Arundel to instruct his son William Howard in mathematics. Some of Oughtred's mathematical correspondence survives, and is printed in Bayle's General Dictionary, and in Rigaud's Correspondence of Scientific Men. William Alabaster wrote to him in 1633 to propose the quadrature of the circle by consideration of the fourth chapter of the Book of Ezekiel. In 1634 he corresponded with the French architect François Derand, and with Sir Charles Cavendish, Johannes Banfi Hunyades, William Gascoigne and Dr John Twysden, M.D..
Oughtred offered free mathematical tuition to pupils, among them Richard Delamain and Jonas Moore, and his teaching influenced a generation of mathematicians. Seth Ward resided with Oughtred for six months to learn contemporary mathematics, and the physician Charles Scarborough also stayed at Albury: John Wallis and Christopher Wren corresponded with him. Another Albury pupil was Robert Wood, who helped him to see the Clavis through the press. Isaac Newton's high opinion of Oughtred is expressed in his letter of 1694 to Nathaniel Hawes, where he quotes him extensively, calling him "a Man whose judgement may safely be relyed upon... that very good and judicious man, Mr Oughtred".
The first edition of John Wallis's foundational text on infinitesimal calculus, Arithmetica Infinitorum, carries a long letter of dedication to William Oughtred.
Publications
''Clavis Mathematicæ'' (1631)
William Oughtred's most important work was first published in 1631, in Latin, under the title Arithemeticæ in Numeris et Speciebus Institutio, quae tum Logisticæ, tum Analyticæ, atque adeus totius Mathematicæ quasi Clavis est. It was dedicated to William Howard, youngest son of Oughtred's patron Thomas Howard, 14th Earl of Arundel.This is a textbook on elementary algebra. It begins with a discussion of the Hindu-Arabic notation of decimal fractions and later introduces multiplication and division sign abbreviations of decimal fractions. Oughtred also discussed two ways to perform long division and introduced the "~" symbol, in terms of mathematics, expressing the difference between two variables. Clavis Mathematicae became a classic, reprinted in several editions. It was used as a textbook by John Wallis and Isaac Newton among others. A concise work, it argued for a less verbose style in mathematics, and greater dependence on symbols. Drawing on François Viète, Oughtred also innovated freely with symbols, introducing not only the multiplication sign as now used universally, but also the proportion sign. The first edition, 1631, contained 20 chapters and 88 pages including algebra and various fundamentals of mathematics.
The work was recast for the New Key, which appeared first in an English edition of 1647, The Key of the Mathematicks New Forged and Filed, dedicated to Sir Richard Onslow and to his son Arthur Onslow, and then in a Latin edition of 1648, entitled Clavis Mathematica Denuo Limata, sive potius Fabricata, in which the preface was removed and the book was reduced by one chapter. In the English Foreword, Oughtred explains that the intention had always been to provide the ingenious reader with an Ariadne's thread through the intricate labyrinth of these studies, but that his earlier, highly compressed style had been found difficult by some, and was now further elucidated. These editions contained additional tracts on the resolution of adfected equations proposed in numbers, and other materials necessary for the use of decimal parts and logarithms, as well as his work on delineating sundials.
The last lifetime edition was in 1652, and posthumous editions appeared in 1667 and 1693, and in 1694. The work gained popularity around 15 years after it first appeared, as mathematics took a greater role in higher education. Wallis wrote the introduction to his 1652 edition, and used it to publicise his skill as cryptographer; in another, Oughtred promoted the talents of Wren.