**William Oughtred** was an English mathematician who is best known for his invention of an early form of the slide rule. He invented many new symbols including X for multiplication and :: for proportion.

- We have given William's date of birth as 5 March 1574, and indeed most biographies give this as his date of birth, but in fact it is the date that he was baptised.
- It is surprising that although very little mathematics was taught at either Eton or Cambridge at this time, Oughtred became passionately interested.
- Although Oughtred did not publish any mathematics during his years at Cambridge, nevertheless we know that he did produce various writings which he published much later.
- Oughtred was ordained a Church of England minister in 1603 but he continued as a fellow at Cambridge University until 1604 when he became vicar of Shalford, Surrey, a village south of Gilford.
- Two of his sons, Benjamin and John, shared Oughtred's interest in instruments and became watchmakers.
- In 1610, Oughtred became rector of Albury, a village about 5 km east of Shalford.
- Oughtred's marriage had brought him into contact with certain local families which influenced his position.
- Francis Aungier (1558-1632) was 1st Baron of Longford and Oughtred taught his son, Gerald Aungier (1596-1655), mathematics.
- Oughtred, of course, was also a Latin scholar and, as others of this period, would write his works in Latin.
- In 1620 Oughtred met Captain Marmaduke Neilson who claimed to have found an astronomical method of finding longitude at sea.
- It seems that at this time it was agreed that Neilson's method would not work but, some years later Oughtred would become more formally involved with assessing Neilson's method.
- It was in 1628 that Oughtred made an important contact which allowed him to become more involved with the mathematicians working in London.
- This gave Oughtred a base in London which was important to him.
- William Howard was a bright boy and Oughtred taught him advanced mathematics.
- To assist in this teaching, Oughtred composed a work on mathematics which was published in 1631 as Clavis Mathematicae Ⓣ(Key to mathematics).
- Oughtred took private pupils who came to his house in Albury and lived there free of charge while they received mathematical instruction.
- Christopher Brookes, one of Allen's assistants, became Oughtred's son-in-law.
- He edited Oughtred's The Solution of All Spherical Triangles by the Planisphere (1651).
- Although Oughtred had not had instruments made early in his career, he had invented them while at Cambridge.
- One of his pupils at Albury, William Forster, spent the summer of 1630 living in Oughtred's home and was so impressed with Oughtred's mathematical instruments that he persuaded Oughtred to let him publish an English translation of Oughtred's unpublished Latin description.
- Both invented, and the uses of both written in Latin by Mr William Oughtred.
- Translated into English and set forth for the public benefit by William Forster.
- Although, as we have seen, Oughtred gained from the support of Thomas Howard, 21st Earl of Arundel, nevertheless he felt that he never received the rewards that he deserved from his patron.
- Others too considered Arundel less than generous in his dealings with Oughtred who looked for church preferments.
- We mentioned above that Oughtred would become involved with Captain Marmaduke Neilson later and this happened in 1636.
- A commission composed of Sir James Galloway, John Seldon, Henry Gellibrand and William Oughtred was set up "to consider and certify whether they hold the petitioner able to perform the particulars mentioned in his petition." The commission's report has not survived but we can be certain that the commission did not find Neilson's method workable.
- Our description of Oughtred's life makes it appear that it was a busy one for, we must remember, his full-time position was as rector of Albury.
- Florian Cajori studied Oughtred's writings carefully and was able to gain a useful feeling for both his approach to mathematics and to teaching mathematics.
- In studying the ancient authors Oughtred is reported to have written down on the margin of the printed page some of the theorems and their proofs, expressed in the symbolic language of algebra.
- Oughtred's most important work, Clavis Mathematicae Ⓣ(Key to mathematics) (1631), included a description of Hindu-Arabic notation and decimal fractions but one of the real strengths of the work is the way that fractions, irrationals, decimal expansions, and logarithms are all treated as "numbers." This was in contrast with other mathematicians at this time who treated these as distinct concepts.
- Like all Oughtred's works it was very condensed containing only 88 pages.
- Oughtred used π in Clavis Mathematicae Ⓣ(Key to mathematics) but not for the ratio of the circumference to the diameter, merely for the circumference.
- Today it seems that Oughtred is best known for his invention of an early form of the slide rule.
- In 1630 Oughtred invented a circular slide rule.
- Delamain certainly published a description of a circular slide rule before Oughtred.
- Unfortunately a very heated argument ensued and to some extent this formed a cloud over the later years of Oughtred's life.
- Oughtred's other works were Trigonometria (1657), one of the first works on trigonometry to use concise symbolism, The Solution of All Spherical Triangles by the Planisphere (1651), solving spherical triangles by the planisphere, and a number of more minor works on watchmaking and methods to determine the position of the sun published posthumously as Opuscula mathematica Ⓣ(Mathematical works) (1677).
- The English Civil War (1642-1646) was a difficult time for Oughtred who was a staunch royalist supporter.
- William Lilly (1602-1681) was a parliamentary astrologer whose support of Oughtred was a factor in having him spared.
- Oughtred owned an important library which went in part to William Jones but it is impossible today to identify the books that came from Oughtred's library.

Born 5 March 1574, Eton, Buckinghamshire, England. Died 13 June 1660, Albury, Surrey, England.

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Analysis, Geometry, Origin England, Number Theory, Special Numbers And Numerals

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive