Oughtred, William

William Oughtred, (born March 5, 1574, Eton, Buckinghamshire, England—died June 30, 1660, Albury, Surrey), English mathematician and Anglican minister who invented the earliest form of the slide rule, two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner sliding rule came later.

Oughtred was educated at Eton College and at King’s College, Cambridge, where he received his bachelor’s degree (1596) and master’s degree (1600). Before his ordainment as an Anglican priest in 1603 and appointment as vicar of Shalford in 1604, Oughtred had already designed (or improved upon) several instruments and composed various works that would be published much later. In 1610 he became rector of Albury, where he remained until his death.

Oughtred was extremely generous in assisting anyone desirous of instruction in mathematics, refusing to accept any remuneration for such instruction. For more than five decades he tutored some of the better-known English mathematicians, such as John Wallis, John Pell, and Seth Ward, as well as numerous teachers of mathematics and instrument-makers who practiced in London. In addition, he kept abreast of the mathematical sciences on the Continent, and either through correspondence or by word of mouth he assisted in the diffusion of French and Italian results among English practitioners.

As a clergyman, Oughtred was reluctant to publish on mathematics. However, in 1631 he consented to allow the printing of a small manual that he had utilized in teaching one of his students. The book became famous under the title of Clavis Mathematicae (“The Key to Mathematics”), although it was not an easy text. It compressed much of contemporary European knowledge of arithmetic and algebra into less than 100 pages (in the first edition), while a somewhat obscure style and a penchant for excessive symbolism made the dense text even more challenging. Of the many symbols Oughtred introduced only two are still widely used, “×” for multiplication and “::” for proportion. Despite its difficulty, the book quickly became one of the most popular mathematics textbooks in 17th-century England. It was often reprinted both in Latin and in the vernacular, and it exerted a formative influence on, among others, the chemist Robert Boyle (1627–91), the architect Christopher Wren (1632–1723), and the mathematician-physicist Isaac Newton (1643–1727). Oughtred’s other writings were published by his students much later, including Trigonometria (1657; “Trigonometry”) and a posthumous collection of tracts, Opuscula mathematica hactenus inedita (1677; “Unpublished Mathematical Papers”).

Shortly after the publication of the Clavis Mathematicae, Oughtred became embroiled in a bitter priority dispute over instrument design. In the early 1620s, improving upon a logarithmic scale invented by Edmund Gunter, Oughtred designed the circular slide rule. However, in 1630 a former student of his and tutor to King Charles I of Great Britain, Richard Delamain, published a small pamphlet in which he claimed to have invented that instrument, and an acrimonious controversy ensued. Oughtred described his circular slide rule in Circles of Proportion and the Horizontal Instrument (1632), which, in addition to defending his reputation and priority during the controversy, addressed the important issue of the proper role of theory and instruments in the teaching of mathematics—a subject of continuing debate.