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William Oughtred (5 March 1574 – 30 June 1660) was an English mathematician.

After John Napier invented logarithms, and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, it was Oughtred who first used two such scales sliding by one another to perform direct multiplication and division; and he is credited as the inventor of the slide rule in 1622. Oughtred also introduced the "×" symbol for multiplication as well as the abbreviations "sin" and "cos" for the sine and cosine functions.[1]


Oughtred was born at Eton in Buckinghamshire (now part of Berkshire), and educated there and at King's College, Cambridge, of which he became fellow.[2] Being admitted to holy orders, he left the University of Cambridge about 1603, for a living at Shalford; he was presented in 1610 to the rectory of Albury, near Guildford in Surrey, where he settled. About 1628 he was appointed by the Earl of Arundel to instruct his son in mathematics.

He corresponded with some of the most eminent scholars of his time, including William Alabaster, Sir Charles Cavendish, and William Gascoigne.[3][4] He kept up regular contacts with Gresham College, where he knew Henry Briggs and Gunter.[5]

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.[6] Another Albury pupil was Robert Wood, who helped him get the Clavis through the press.[7]

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.[8][9]

He remained rector until his death in 1660 at Albury, a month after the restoration of Charles II.[10]

Interest in the occult

Oughtred had an interest in alchemy and astrology.[11] 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.[12][13] In fact Oughtred was protected at this time by Bulstrode Whitelocke.[14]

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.[15][16] 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.



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 ::).[17] 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;[18] 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.[19]

* 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.[20]
* Trigonometria with Canones sinuum (1657).

Slide rules

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.[21] 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.[22]

Sun dials

He invented the double horizontal sundial, now named Oughtred-type after him.[23] 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 and Jean Leurechon. That translation itself is no longer attributed to Oughtred, but (probably) to Francis Malthus.[24]


1. ^ Florian Cajori (1919). A History of Mathematics. Macmillan.
2. ^ Oughtred, William in Venn, J. & J. A., Alumni Cantabrigienses, Cambridge University Press, 10 vols, 1922–1958.
3. ^
4. ^
5. ^
6. ^ Helena Mary Pycior, Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick (1997), p. 42.
7. ^ Toby Christopher Barnard, Cromwellian Ireland: English Government and Reform in Ireland 1649-1660 (2000), p. 223.
8. ^ Michelle Selinger, Teaching Mathematics (1994), p. 142.
9. ^
10. ^
11. ^ Keith Thomas, Religion and the Decline of Magic (1973), p. 322 and note p. 452.
12. ^;dir=hutto_dicti_078_en_1795;step=textonly
13. ^ 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
14. ^
15. ^ Historico-Critical Inquiry into the Origins of the Rosicrucians and the Free-Masons
16. ^ E.g. William Wynn Westcott, The Rosicrucians, Past and Present, at Home and Abroad, p. 426.
17. ^ Helena Mary Pycior, Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick (1997), p. 48.
18. ^
19. ^
20. ^ Dictionary of National Biography, article on Forster.
21. ^
22. ^,805,The_slide_rule_-_a_forgotten_tool
23. ^ 24. ^

This article incorporates text from the Encyclopædia Britannica, Eleventh Edition, a publication now in the public domain.

Further reading

* Florian Cajori (1916), William Oughtred, a great seventeenth-century teacher of mathematics online text
* Jacqueline Anne Stedall, Ariadne's Thread: The Life and Times of Oughtred's Clavis, Annals of Science, Volume 57, Issue 1 January 2000, pp. 27–60.

External links

* O'Connor, John J.; Robertson, Edmund F., "William Oughtred", MacTutor History of Mathematics archive, University of St Andrews, .
* Galileo Project page
* The Oughtred Society inspired by Oughtred and dedicated to the history and preservation of slide rules.
* article with additional material on Oughtred.
* Account of Oughtred by John Aubrey

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