William Oughtred

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William Oughtred
Wenceslas Hollar - William Oughtred.jpg
William Oughtred engraving by Wenceslaus Hollar
Born5 March 1574
Eton, Buckinghamshire, England
Died30 June 1660(1660-06-30) (aged 86)
Albury, Surrey, England
EducationEton College
Alma materKing's College, Cambridge
Known forSlide rule
Multiplication "×" sign
Scientific career
InstitutionsKing's College, Cambridge
Notable studentsJohn Wallis
Christopher Wren
Richard Delamain
Seth Ward

William Oughtred (/ˈɔːtərd/ AWT-ed;[1][2] 5 March 1574 – 30 June 1660[2]) was an English mathematician and Anglican clergyman. After John Napier invented logarithms and Edmund Gunter created the logarithmic scales (lines, or rules) 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.[3] He also introduced the "×" symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions.[4]

Early life[edit]

Oughtred was born at Eton in Buckinghamshire (now part of Berkshire), and educated at Eton College and King's College, Cambridge of which he became fellow.[5] Being admitted to holy orders, he left the University of Cambridge about 1603, for a living at Shalford in Surrey; he was presented in 1610 to the rectory of Albury, near Guildford in Surrey, where he settled. He was rector of Albury for fifty years.[citation needed]

Marriage and children[edit]

On 20 February 1606, he married Christsgift Caryll, (niece) of the Caryll family of Tangley Hall at Wonersh[6] in Surrey, of which Lady Elizabeth Aungier (daughter of Sir Francis), wife of Simon Caryll 1607-1619, was matriarch and then dowager until her death in about 1650.[7] They 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 his sons, Benjamin and John, shared Oughtred's interest in instruments and became watchmakers.[8]


About 1628 he was appointed by the Earl of Arundel to instruct his son in mathematics.[9] He corresponded with some of the most eminent scholars of his time, including William Alabaster, Sir Charles Cavendish, and William Gascoigne.[10][11] He kept up regular contacts with Gresham College, where he knew Henry Briggs and Gunter.[12]

He offered free mathematical tuition to pupils, who included Richard Delamain, and Jonas Moore, making him an influential teacher of a generation of mathematicians. Seth Ward resided with Oughtred for six months to learn contemporary mathematics, and the physician Charles Scarburgh also stayed at Albury; John Wallis, and Christopher Wren corresponded with him.[13] Another Albury pupil was Robert Wood, who helped him get the Clavis through the press.[14]

The invention of the slide rule involved Oughtred in a priority dispute with Delamain. They also disagreed on pedagogy in mathematics, with Oughtred arguing that theory should precede practice.[15][16]

He remained rector until his death in 1660 at Albury, a month after the restoration of Charles II. He was buried in Old St Peter and St Paul's Church, Albury.[17]

Interest in the occult[edit]

Oughtred had an interest in alchemy and astrology.[18] The testimony for his occult activities is quite slender, but there has been an accretion to his reputation based on his contemporaries.

According to John Aubrey, he was not entirely sceptical about astrology. William Lilly, an eminent astrologer, claimed in his autobiography to have intervened on behalf of Oughtred to prevent his ejection by Parliament in 1646.[19][20] In fact, Oughtred was protected at this time by Bulstrode Whitelocke.[21] Aubrey states that (despite their political differences) he was also defended by Sir Richard Onslow.[22]

Elias Ashmole was (according to Aubrey) a neighbour in Surrey, though Ashmole's estates acquired by marriage were over the county line in Berkshire; and Oughtred's name has been mentioned in purported histories of early freemasonry, a suggestion that Oughtred was present at Ashmole's 1646 initiation going back to Thomas De Quincey.[23][24] It was used by George Wharton in publishing The Cabal of the Twelve Houses astrological by Morinus (Jean-Baptiste Morin) in 1659.

He expressed millenarian views to John Evelyn, as recorded in Evelyn's Diary, entry for 28 August 1655.[citation needed]


Oughtred's name is remembered in the Oughtred Society, a group formed in the United States in 1991 for collectors of slide rules. It produces the twice-yearly Journal of the Oughtred Society and holds meetings and auctions for its members.[25][26]


Clavis mathematicae, 1652


He published, among other mathematical works, Clavis Mathematicae (The Key to Mathematics), in 1631. It became a classic, reprinted in several editions, and used by Wallis and Isaac Newton amongst others. It was not ambitious in scope, but an epitome aiming to represent current knowledge of algebra concisely. It argued for a less verbose style of mathematics, with a greater dependence on symbols; drawing on François Viète (though not explicitly), Oughtred also innovated freely in symbols, introducing not only the multiplication sign as now used universally, but also the proportion sign (double colon ::).[27] The book became popular around 15 years later, 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;[28] in another, Oughtred promoted the talents of Wren.

Other works were a treatise on navigation entitled Circles of Proportion, in 1632, and a book on trigonometry and dialling, and his Opuscula Mathematica, published posthumously in 1676. He invented a universal equinoctial ring dial of two rings.[29]

  • Clavis Mathematicae (1631) further Latin editions 1648, 1652, 1667, 1693; first English edition 1647.
  • Circles of Proportion and the Horizontal Instrument (1632); this was edited by his pupil, William Forster.[30]
  • Trigonometria with Canones sinuum (1657).

Slide rules[edit]

Oughtred's invention of the slide rule consisted of taking a single "rule", already known to Gunter, and simplifying the method used to employ it. Gunter required the use of a pair of dividers, to lay off distances on his rule; Oughtred made the step of sliding two rules past each other to achieve the same ends.[31] His original design of some time in the 1620s was for a circular slide rule; but he was not the first into print with this idea, which was published by Delamain in 1630. The conventional design of a sliding middle section for a linear rule was an invention of the 1650s.[32]

Sun dials[edit]

He invented the double horizontal sundial, now named Oughtred-type after him.[33] A short description The description and use of the double Horizontall Dyall (16 pages) was added to a 1653 edition (in English translation) of the pioneer book on recreational mathematics, Récréations Mathématiques (1624) by Hendrik van Etten, a pseudonym of Jean Leurechon. The translation itself is no longer attributed to Oughtred, but (probably) to Francis Malthus.[34]

He also invented the Universal equinoctial ring dial.[35]


  1. ^ How to Pronounce: Oughtred Society Retrieved 9 August 2018.
  2. ^ a b Smith, David Eugene (1923). History of Mathematics. 1. p. 392.
  3. ^ Smith, David E. (1958). History of Mathematics. Courier Corporation. p. 205. ISBN 9780486204307.
  4. ^ Florian Cajori (1919). A History of Mathematics. Macmillan.
  5. ^ "Oughtred, William (OTRT592W)". A Cambridge Alumni Database. University of Cambridge.
  6. ^ ODNB, and see Aubrey's Brief Lives, Ed. Oliver Lawson Dick (Ann Arbor, Michigan 1962), pp. 222-224.
  7. ^ 1623 Harleian Visitation of Surrey, Harl Soc. Vol. XLIII (1899), pp. 88–89: cf. C. P. C. wills of John Machell, 1647; Elizabeth Machell, 1650/1656.
  8. ^ "Oughtred biography". www-groups.dcs.st-and.ac.uk.
  9. ^ Chisholm 1911.
  10. ^ "Janus: Oughtred, William (? 1574-1660) mathematician". Janus.lib.cam.ac.uk. Retrieved 31 October 2012.
  11. ^ "DSpace at Cambridge: Letter from William Gascoigne to William Oughtred". Dspace.cam.ac.uk. 13 June 2007. Retrieved 31 October 2012.
  12. ^ "Loading..." www.compilerpress.atfreeweb.com.
  13. ^ Helena Mary Pycior, Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick (1997), p. 42.
  14. ^ Toby Christopher Barnard, Cromwellian Ireland: English Government and Reform in Ireland 1649-1660 (2000), p. 223.
  15. ^ Michelle Selinger, Teaching Mathematics (1994), p. 142.
  16. ^ "The Galileo Project". Galileo.rice.edu. Retrieved 31 October 2012.
  17. ^ "Parishes – Albury | A History of the County of Surrey: Volume 3 (pp. 72–77)". British-history.ac.uk. 22 June 2003. Retrieved 31 October 2012.
  18. ^ Keith Thomas, Religion and the Decline of Magic (1973), p. 322 and note p. 452.
  19. ^ "Archimedes Project". Archimedes.mpiwg-berlin.mpg.de. Retrieved 31 October 2012.
  20. ^ About this time, the most famous mathematician of all Europe,[16] 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. from https://www.gutenberg.org/files/15835/15835-8.txt
  21. ^ "Biography" (PDF). www.clas.ufl.edu.
  22. ^ O.L. Dick, Aubrey's Brief Lives (Ann Arbor Michigan 1962), p. 224.
  23. ^ Historico-Critical Inquiry into the Origins of the Rosicrucians and the Free-Masons
  24. ^ E. g. William Wynn Westcott, The Rosicrucians, Past and Present, at Home and Abroad, p. 426.
  25. ^ "The Oughtred Society". The Oughtred Society. Retrieved 18 March 2015.
  26. ^ "Brochure" (PDF). The Oughtred Society. Retrieved 18 March 2015.
  27. ^ Helena Mary Pycior, Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick (1997), p. 48.
  28. ^ "Oxford Figures, Chapter 1: 800 years of mathematical traditions". Mathematical Institute – University of Oxford. 17 September 2007. Archived from the original on 26 October 2012. Retrieved 31 October 2012.
  29. ^ "National Maritime Museum". Nmm.ac.uk. Retrieved 31 October 2012.
  30. ^  Stephen, Leslie, ed. (1889). "Forster, William (fl.1632)". Dictionary of National Biography. 20. London: Smith, Elder & Co.
  31. ^ "Slide Rules". Hpmuseum.org. Retrieved 31 October 2012.
  32. ^ "The slide rule – a forgotten tool". Powerhouse Museum Collection. Retrieved 31 October 2012.
  33. ^ "Harvard University – Department of History of Science". Dssmhi1.fas.harvard.edu. Archived from the original on 20 February 2012. Retrieved 31 October 2012.
  34. ^ Heefer, Albrecht. "Récréations Mathématiques (1624) A Study on its Authorship, Sources and Influence" (PDF). logica.ugent.be.
  35. ^ "Royal Museums Greenwich".

Wikisource Chisholm, Hugh, ed. (1911). "Oughtred, William". Encyclopædia Britannica (11th ed.). Cambridge University Press.

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