William Oughtred
Encyclopedia
William Oughtred was an English
mathematician
.
After John Napier
invented logarithm
s, and Edmund Gunter
created the logarithmic scale
s (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.
in Buckinghamshire
(now part of Berkshire
), and educated there and at King's College, Cambridge
, of which he became fellow. 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. He married Christsgift Caryll, (niece) of the Caryll family of Tangley Hall at Wonersh
, of which Lady Elizabeth Aungier (daughter of Sir Francis
), wife of Simon Caryll 1607-1619, was matriarch and then dowager until her death c.1650.
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
. He kept up regular contacts with Gresham College
, where he knew Henry Briggs
and Gunter
.
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. Another Albury pupil was Robert Wood
, who helped him get the Clavis through the press.
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.
He remained rector until his death in 1660 at Albury, a month after the restoration of Charles II
.
and astrology
. 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. In fact Oughtred was protected at this time by Bulstrode Whitelocke
. Aubrey states that (despite their political differences) he was also defended by Sir Richard Onslow
.
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
. 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.
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 ::). 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; 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.
, Récréations Mathématiques (1624) by Hendrik van Etten and Jean Leurechon. That translation itself is no longer attributed to Oughtred, but (probably) to Francis Malthus.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
After John Napier
John Napier
John Napier of Merchiston – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish mathematician, physicist, astronomer & astrologer, and also the 8th Laird of Merchistoun. He was the son of Sir Archibald Napier of Merchiston. John Napier is most renowned as the discoverer...
invented logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
s, and Edmund Gunter
Edmund Gunter
Edmund Gunter , English mathematician, of Welsh descent, was born in Hertfordshire in 1581.He was educated at Westminster School, and in 1599 was elected a student of Christ Church, Oxford. He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity...
created the logarithmic scale
Logarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...
s (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
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
and division
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
; 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
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
and cosine functions.
Life
Oughtred was born at EtonEton, Berkshire
Eton is a town and civil parish in Berkshire, England, lying on the opposite bank of the River Thames to Windsor and connected to it by Windsor Bridge. The parish also includes the large village of Eton Wick, 2 miles west of the town, and has a population of 4,980. Eton was in Buckinghamshire until...
in Buckinghamshire
Buckinghamshire
Buckinghamshire is a ceremonial and non-metropolitan home county in South East England. The county town is Aylesbury, the largest town in the ceremonial county is Milton Keynes and largest town in the non-metropolitan county is High Wycombe....
(now part of Berkshire
Berkshire
Berkshire is a historic county in the South of England. It is also often referred to as the Royal County of Berkshire because of the presence of the royal residence of Windsor Castle in the county; this usage, which dates to the 19th century at least, was recognised by the Queen in 1957, and...
), and educated there and at King's College, Cambridge
King's College, Cambridge
King's College is a constituent college of the University of Cambridge, England. The college's full name is "The King's College of our Lady and Saint Nicholas in Cambridge", but it is usually referred to simply as "King's" within the University....
, of which he became fellow. Being admitted to holy orders, he left the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
about 1603, for a living at Shalford
Shalford
Shalford may refer to:Places in England*Shalford, Essex*Shalford, Somerset*Shalford, SurreyOther*HMS Shalford, a Ford class seaward defence boat of the Royal Navy...
; he was presented in 1610 to the rectory of Albury
Albury, Surrey
Albury is a village and civil parish in the borough of Guildford in Surrey, England, about south-east of Guildford town centre. The village is within an Area of Outstanding Natural Beauty and Site of Special Scientific Interest....
, near Guildford
Guildford
Guildford is the county town of Surrey. England, as well as the seat for the borough of Guildford and the administrative headquarters of the South East England region...
in Surrey
Surrey
Surrey is a county in the South East of England and is one of the Home Counties. The county borders Greater London, Kent, East Sussex, West Sussex, Hampshire and Berkshire. The historic county town is Guildford. Surrey County Council sits at Kingston upon Thames, although this has been part of...
, where he settled. He married Christsgift Caryll, (niece) of the Caryll family of Tangley Hall at Wonersh
Wonersh
Wonersh is a small Surrey village in England. Wonersh is about 3 miles SSE of Guildford on the B2128 road from Guildford, Shalford to Cranleigh...
, of which Lady Elizabeth Aungier (daughter of Sir Francis
Francis Aungier, 1st Baron Aungier of Longford
Sir Francis Aungier, 1st Baron Aungier of Longford , also known as Lord Aungier, was the progenitor of the Earldom of Longford, member of the House of Lords, Privy Councillor for Ireland, and Master of the Rolls in Ireland under James I and Charles I.-Early life:Francis was born in 1558 in...
), wife of Simon Caryll 1607-1619, was matriarch and then dowager until her death c.1650.
About 1628 he was appointed by the Earl of Arundel
Thomas Howard, 21st Earl of Arundel
Thomas Howard, 21st Earl of Arundel KG, was a prominent English courtier during the reigns of King James I and King Charles I, but he made his name as a Grand Tourist and art collector rather than as a politician. When he died he possessed 700 paintings, along with large collections of sculpture,...
to instruct his son in mathematics. He corresponded with some of the most eminent scholars of his time, including William Alabaster
William Alabaster
William Alabaster was an English poet, playwright, and religious writer. His surname is one of the many variants of "arbalester", a crossbowman....
, Sir Charles Cavendish, and William Gascoigne
William Gascoigne (scientist)
William Gascoigne was an English astronomer, mathematician and maker of scientific instruments from Middleton near Leeds who invented the micrometer...
. He kept up regular contacts with Gresham College
Gresham College
Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in central London, England. It was founded in 1597 under the will of Sir Thomas Gresham and today it hosts over 140 free public lectures every year within the City of London.-History:Sir Thomas Gresham,...
, where he knew Henry Briggs
Henry Briggs
Henry Briggs may refer to:*Henry Briggs *Henry Briggs , *Henry Shaw Briggs , Union general in the American Civil War...
and Gunter
Edmund Gunter
Edmund Gunter , English mathematician, of Welsh descent, was born in Hertfordshire in 1581.He was educated at Westminster School, and in 1599 was elected a student of Christ Church, Oxford. He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity...
.
He offered free mathematical tuition to pupils, who included Richard Delamain, and Jonas Moore
Jonas Moore
Sir Jonas Moore, FRS was an English mathematician, surveyor, Ordnance Officer and patron of astronomy. He participated in two of the most ambitious English civil engineering projects of the 17th century: the draining of the Great Level of the Fens and the building of the Mole at Tangier...
, making him an influential teacher of a generation of mathematicians. Seth Ward
Seth Ward (bishop)
Seth Ward was an English mathematician, astronomer, and bishop.-Early life:He was born in Hertfordshire, and educated at Sidney Sussex College, Cambridge, where he graduated B.A. in 1636 and M.A. in 1640, becoming a Fellow in that year...
resided with Oughtred for six months to learn contemporary mathematics, and the physician Charles Scarburgh also stayed at Albury; John Wallis, and Christopher Wren
Christopher Wren
Sir Christopher Wren FRS is one of the most highly acclaimed English architects in history.He used to be accorded responsibility for rebuilding 51 churches in the City of London after the Great Fire in 1666, including his masterpiece, St. Paul's Cathedral, on Ludgate Hill, completed in 1710...
corresponded with him. Another Albury pupil was Robert Wood
Robert Wood (mathematician)
-Life:Born at Pepperharrow, near Godalming in Surrey, in 1621 or 1622, was the son of Robert Wood , rector of Pepperharrow. He was educated at Eton College, and matriculated from New Inn Hall on 3 July 1640. Obtaining one of the Eton postmasterships at Merton College in 1642, he graduated B. A....
, who helped him get the Clavis through the press.
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.
He remained rector until his death in 1660 at Albury, a month after the restoration of Charles II
Charles II of England
Charles II was monarch of the three kingdoms of England, Scotland, and Ireland.Charles II's father, King Charles I, was executed at Whitehall on 30 January 1649, at the climax of the English Civil War...
.
Interest in the occult
Oughtred had an interest in alchemyAlchemy
Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher's stone possessing powers including the capability of turning base...
and astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
. 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
John Aubrey
John Aubrey FRS, was an English antiquary, natural philosopher and writer. He is perhaps best known as the author of the collection of short biographical pieces usually referred to as Brief Lives...
, he was not entirely sceptical about astrology. William Lilly
William Lilly
William Lilly , was an English astrologer famed during his time. Lilly was particularly adept at interpreting the astrological charts drawn up for horary questions, as this was his speciality....
, an eminent astrologer, claimed in his autobiography to have intervened on behalf of Oughtred to prevent his ejection by Parliament in 1646. In fact Oughtred was protected at this time by Bulstrode Whitelocke
Bulstrode Whitelocke
Sir Bulstrode Whitelocke was an English lawyer, writer, parliamentarian and Lord Keeper of the Great Seal of England.- Biography :...
. Aubrey states that (despite their political differences) he was also defended by Sir Richard Onslow
Richard Onslow (Parliamentarian)
Sir Richard Onslow was an English Member of Parliament and fought on the Parliamentary side during the English Civil War. He was the grandson of one Speaker of the House of Commons and the grandfather of another, both also called Richard Onslow.Onslow was knighted on 2 June 1624...
.
Elias Ashmole
Elias Ashmole
Elias Ashmole was a celebrated English antiquary, politician, officer of arms, astrologer and student of alchemy. Ashmole supported the royalist side during the English Civil War, and at the restoration of Charles II he was rewarded with several lucrative offices.Ashmole was an antiquary with a...
was (according to Aubrey) a neighbour in Surrey
Surrey
Surrey is a county in the South East of England and is one of the Home Counties. The county borders Greater London, Kent, East Sussex, West Sussex, Hampshire and Berkshire. The historic county town is Guildford. Surrey County Council sits at Kingston upon Thames, although this has been part of...
, though Ashmole's estates acquired by marriage were over the county line in Berkshire
Berkshire
Berkshire is a historic county in the South of England. It is also often referred to as the Royal County of Berkshire because of the presence of the royal residence of Windsor Castle in the county; this usage, which dates to the 19th century at least, was recognised by the Queen in 1957, and...
; and Oughtred's name has been mentioned in purported histories of early freemasonry
Freemasonry
Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around six million, including approximately 150,000 under the jurisdictions of the Grand Lodge...
, a suggestion that Oughtred was present at Ashmole's 1646 initiation going back to Thomas De Quincey
Thomas de Quincey
Thomas Penson de Quincey was an English esssayist, best known for his Confessions of an English Opium-Eater .-Child and student:...
. 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
John Evelyn
John Evelyn was an English writer, gardener and diarist.Evelyn's diaries or Memoirs are largely contemporaneous with those of the other noted diarist of the time, Samuel Pepys, and cast considerable light on the art, culture and politics of the time John Evelyn (31 October 1620 – 27 February...
, as recorded in Evelyn's Diary, entry for 28 August 1655.
Books
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 NewtonIsaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
amongst others. It was not ambitious in scope, but an epitome
Epitome
An epitome is a summary or miniature form; an instance that represents a larger reality, also used as a synonym for embodiment....
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
François Viète
François Viète , Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations...
(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 ::). 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; in another, Oughtred promoted the talents of Wren.
Other works were a treatise on navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
entitled Circles of Proportion, in 1632, and a book on trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
and dialling
Dialling
Dialling or dialing usually means to make a telephone call by operating its rotary dial.-Etymology:The word, dial, comes from the Latin dialis = "daily", because a sundial throws a shadow related to the time of day...
, and his Opuscula Mathematica, published posthumously in 1676. He invented a universal equinoctial ring dial of two rings.
- 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.
- 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. 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.Sun dials
He invented the double horizontal sundial, now named Oughtred-type after him. 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 mathematicsRecreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
, Récréations Mathématiques (1624) by Hendrik van Etten and Jean Leurechon. That translation itself is no longer attributed to Oughtred, but (probably) to Francis Malthus.
Further reading
- Florian CajoriFlorian CajoriFlorian Cajori was one of the most celebrated historians of mathematics in his day.- Biography :...
(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
- Galileo Project page
- The Oughtred Society inspired by Oughtred and dedicated to the history and preservation of slide rules.
- Answers.com article with additional material on Oughtred.
- Account of Oughtred by John Aubrey