John Kersey

Quick Info

23 November 1616
Bodicote, near Banbury, Oxfordshire, England
20 May 1677
London, England

John Kersey was a 17th century English mathematician who is most famed for his book Elements of that Mathematical Art Commonly called Algebra (1673). He also made many additions to the 1650 edition of Wingate's Arithmetique.


Let us begin by saying a little about the dates we have given for John Kersey's birth and death. The date we have given for his birth, 23 November 1616, is actually the date of his baptism. Given rapid baptism that occurred at this time it is likely that his actual date of birth was only a couple of days earlier. We know that he was buried on 23 May 1677, so again following the customs of the time, we can be confident that our guess for his date of death will be fairly accurate. John Kersey was the son of Anthony Kersey or Carsaye (1590-1636) and Alice Fenimore (1594-1622). Anthony and Alice were married on 27 July 1613 in Bodicote, Oxfordshire, England. They had two children, John Kersey, the subject of this biography born 1616, and Jane Kersey baptised 4 April 1619 in Bodicote.

Bodicote is mentioned in [4] (published 1812) where its fame appears to be the chapel and the fact that it was the birthplace of John Kersey:-
Bodicot, or, as it was anciently spelt, Bodycoat, is a hamlet, situated near the road leading from Oxford to Banbury, whose chapel of ease is one of the members of the valuable benefice of Adderbury. At this place was born, in the year 1616, the celebrated mathematician, John Kersey, author of a treatise on Algebra, which still maintains a considerable share of reputation. His baptism is thus recorded in the register appertaining to the chapel:- "John, sonne of Anthony Carsaye and Alice his wife, was baptised the 23rd day of November, Anno Domini 1616." ...
We learn something of Anthony Kersey from his Last will and Testament made shortly before his death in 1636. We note that his wife Alice had died fourteen years earlier so everything he owned was divided between his children. We have modernised the spelling [12]:-
The 24th April Anno Domini 1636.

I Anthony Kersey of Bodicote in the county of Oxfordshire, labourer, being sick of body, but of perfect mind and memory (God be praised), I make and ordain this my Last Will and Testament. ... for my personal estate, I bequeath it as follows.

First I give and bequeath my house, lands and smithy situated at Barford, St Michael in the said Oxfordshire which I lately purchased of Robert Kart and Jenny his wife late of Barford, St Michael aforesaid, unto my son John his heirs and assigns for ever.

I give and bequeath unto my daughter Jane the sum of Thirty pounds of lawful English money, in lieu of half the house, land and smithy abovesaid, to be paid to her by my son John when she comes to the age of 21 years ...

My will is that the remainder of all my goods and chattels, when they are rightly known, shall be equally divided between my said children ...
Alexander Denton (1596-1645) was brought up in the manor house in Hillesden, a village about six km south of Buckingham and 25 km south east of Bodicote. He studied at Christ Church, Oxford, matriculating in 1612, was knighted in 1617 the year he married Mary Hampden, and inherited Hillesden manor on the death of his father in 1633. Alexander and Mary Denton had five sons and eight daughters. They employed John Kersey as a tutor to their sons, particularly for their second son Edmund Denton (1623-1657) born on 28 October 1623. The Denton family were Royalists and their home, the manor house in Hillesden, became the focus of battles in 1644 between Royalist and Parliamentary troops. Cromwell laid siege to the manor in March 1644 and the house was totally destroyed. Alexander Denton was taken prisoner and died in the Tower of London on 1 January 1645. It is unclear whether Kersey was in the manor during the siege or had moved to London earlier. After the destruction of Hillesden manor, Edmund Denton moved to London where he married Elizabeth Rogers on 25 February 1650; they had two children Alexander Denton (1654-1698) and Edmund Denton (1655-1728).

Kersey moved to London in 1644, or somewhat earlier, and lived in Charles Street, near the Covent Garden. He became a teacher of mathematics and a surveyor. Certainly his contacts with the Denton family continued and he felt that it had been the Dentons who had encouraged him to study mathematics in depth. He wrote the following Dedication in his Algebra book, dated 15 April 1673 [11]:-
To Alexander Denton of Hillesden in the County of Buckinghamshire, Esquire, and Mr Edmund Denton his brother; the hopeful blossoms, and only offspring of the truly just and virtuous Edmund Denton Esq.; son and heir of Sir Alexander Denton Kt. A faithful patriot, and eminent sufferer in our late intestine wars, for his loyalty to his late Majesty King Charles the First, of ever-blessed memory: John Kersey, in testimony of his gratitude, for signal favours conferred on him by that noble family; which also gave both birth and nourishment to his mathematical studies, humbly dedicates his labours in this treatise of the Elements of the Algebraic Art.
On 7 September 1653, John Kersey married Mary Perwich (1628-1701) at Saint Mary The Virgin, Aldermanbury, London. Mary had been born on 23 December 1628 in Aldermanbury, London, the daughter of Robert and Susannah Perwich. John and Mary Kersey had a son, also named John Kersey, who was baptised at St Paul, Covent Garden, London on 15 February 1657.

Edmund Wingate (1596-1656) was a mathematician and lawyer who studied at the Queen's College, Oxford from 1610, graduating with a B.A. on 30 June 1614. He was admitted to Gray's Inn on 24 May 1614. He spent some time in Paris, but was living in London, England by the time that the Civil War broke out (1642). He was a supporter of the Parliamentary side and worked with Oliver Cromwell, becoming an MP in 1654. He was the author of several mathematical works and several legal works. In particular he had written the 2-volume work Natural and Artificiall Arithmetique (1630). Cajori in [14] showed that in fact Wingate did not describe the slide rule in that work:-
Some modern writers attribute the invention of the rectilinear slide rule to Edmund Gunter, others to William Oughtred, but most of them to Edmund Wingate. This disagreement is due mainly to lack of opportunity to consult original sources. It is the purpose of this paper to demonstrate that Wingate never wrote on the slide rule, and that Oughtred is the inventor of the rectilinear as well as the circular type.
John Kersey and Edmund Wingate became friends (despite apparently being on the opposite sides in the Civil War). They discussed Wingate's Natural and Artificiall Arithmetique which had two volumes, the second volume being a work showing how to do arithmetic using logarithms while the first volume was simply providing the background information to allow the reader to understand volume 2. Wingate asked Kersey if he would revise the first volume so that it became a general textbook teaching elementary arithmetic. This he did, creating a 480-page book with seven new chapters written by Kersey; it was published as Arithmetique Made Easie (1650). Kersey wrote a Preface to the book [20]:-
And to the end the full knowledge of practical arithmetic in whole numbers might more clearly appear, I have explained divers of the old rules in the first five chapters, and framed anew the rules of division, reduction, and the golden rule, in the Sixth, Seventh, Eighth, and Ninth Chapters; so that now arithmetic in whole numbers is plainly and fully handled before any entrance is made into the craggy paths of fractions, at the sight of which some learners are so discouraged, that they make a stand, and cry out, Non plus ultra, There's no progress farther.
For the complete Preface by Kersey to Arithmetique Made Easie, see THIS LINK.

Wingate himself revised book 2 which appeared in 1652 as Arithmetique Made Easie. The second book. Kersey's version of Book 1 was a great success and it continued to have new editions up to 1760. The success of this work was a major factor in Kersey writing the book Elements of that Mathematical Art Commonly called Algebra (1673-74). He writes in the Preface of that book [11]:-
And the favourable acceptance, which my additions to Mr Wingate's Treatise of Common Arithmetic have found, with divers eminent mathematicians and other lovers of Art, does encourage me to hope, that the younger students of Symbolical Arithmetic and Analytical doctrine, will be well pleased with the following discourse, and that my labours therein will be as candidly accepted, as they have been cordially intended to serve my native Country.
Kersey's book Elements of that Mathematical Art Commonly called Algebra (1673-74) was a great success but, probably ahead of its time, it proved difficult for Kersey to have it published. The book was written by 1667 but by 1672 when he was still seeking contributors, he produced a Synopsis. John Collins strongly supported Kersey's attempt to have the work published and tried both to persuade printers to undertake the work. He also tried hard to get others to subscribe. Collins sent Kersey's Synopsis to Richard Towneley (1629-1707). Towneley lived at Towneley Hall, near Burnley in Lancashire. He was a Roman Catholic so was prevented from holding a university or similar position. He had studied mathematics in the Low Countries and France. Towneley replied to Collins on 13 May 1672 [16]:-
I have shown Mr Kersey's Synopsis to a friend or two, and shall endeavour to procure contributors; however, I shall be one, and wish the other part, you mention in your letter, may soon follow: for want of such books I think is the cause we have so few that understand anything of algebra; I may say so confidently of these parts.
Several at the University of Cambridge, including Isaac Newton, agreed to be contributors. The book was published in the following year. By the time he wrote the Preface to the book (15 April 1673), Kersey was living at The Sign of the Globe in Shandois Street, in Covent Garden, London. In fact we know he lived there from 1670 or earlier. In his Preface he explains that he will describe the Art [11]:-
... called Algebra which first assumes the quantity sought, whether it be a number or a line in a question, as if it were known, and then, with the help of one or more quantities given, proceeds by undeniable consequences, until the quantity which at first was but assumed or supposed to be known, is found equal to some quantity certainly known, and is also known also.

Which analytical way of reasoning produces in conclusion, either a Theorem declaring some Property, Proportion or Equality, justly inferred from things given or granted in a proposition, or else a Canon directing infallibly how that may be found out or done which is desired; and discovers demonstrations of the certainty of the resulting Theorem or Canon, in the Synthetical Method, or by way of composition, by the steps of the Analysis, or Resolution.
For the full Preface see THIS LINK.

Here is an extract from Book 1, Chapter 1:-
In searching out the Solution of a Question by the Algebraic Art, the Number or line sought is usually called a Root, which so long as it remains unknown cannot be really expressed, and therefore it must be designated or represented by some Symbol of Character, at the will of the Artist; also the Powers which may be imagined to proceed from the said Root in such manner as has before been declared are likewise to be represented by Symbols or Characters; concerning which there is much diversity among Algebraical Writers, every one pleasing his Fancy in the choice of Characters: But in this Matter I shall imitate Mr Thomas Harriot in his 'Ars Analytica', and Renates des Cartes [René Descartes] in his 'Geometry', but chiefly the former; whose Method of expressing Quantities by Alphabetical Letters, I conceive to be the plainest for Learners, etc.

To design or represent the Root sought, whether it be a number or a Line in a Question proposed, we may assume any Letter of the Alphabet, as for a, b, or c, etc. but for the better distinguishing of known Quantities from unknown, some Analysts are wont to assume one of the five Vowels, as a, or e, etc. to represent the Quantity sought; and Consonants, as b, c, d, etc. to represent Quantities known or given: Now if the Letter a be assumed to represent the Root sought, then (according to Mr Harriot) the second Power, or the Square raised from that Root, may be represented by aa; the third Power, or the Cube, by aaa; the fourth Power by aaaa; the fifth Power by aaaaa; and after the same manner any higher Power of the Root or Number a may be represented: For so many Dimensions or Degrees as are in the Power, so many times the Letter which at first was assumed for the Root is to be repeated.
For a longer extract from Book 1, Chapter 1, see THIS LINK.

Let us note Kersey does not really deal in negative numbers. He describes -5 as a fictitious number and notes that it could represent a debt. Of course, if one does not deal in negative numbers then aba - b is a bit of a problem. Kersey gets round this by saying that aba - b denotes the excess of aa over bb, but if it is not known which is the greater then he has a symbol (an S rotated 90º anticlockwise) which [11]:-
... signifies the difference of two quantities, to wit, the excess of the greater above the less, when it is not determined or known in which of those quantities the excess lies.
Let us give two examples which are essentially the same but we give them both to emphasise the teaching aspect of the work.

Book 1, Question 14.
There are two numbers the product of whose multiplication is 20 (or b) and the sum of their cubes is 189 (or c). What are the numbers

1. For the greater of the numbers sought put                       a
2. Dividing the given product 20 by a, number left              20/a
3. The cube of the greater number is                                  aaa
4. The cube of the lesser number is                                  8000/aaa
5. Sum of the cubes of the two numbers                     (aaaaaa + 8000)/aaa
6. Which sum must equal 189                                  (aaaaaa + 8000)/aaa = 189
7. Equation after reduction                                  8000 = 189aaa - aaaaaa
8. Resolving the equation in the last step by the canon      a = 5
9. I say that the numbers sought are 5 and 4.

Kersey also, in parallel, gives the more general solution,

a, b/a, aaa, bbb/aaa, (aaaaaa + bbb)/aaa, (aaaaaa + bbb)/aaa = c, bbb = daaa - aaaaaa, ...
Book 1, Question 15.
There are two numbers the product of whose multiplication is 20 (or b) and the difference of their cubes is 61 (or d). What are the numbers?

1. For the greater of the numbers sought put                        a
2. Dividing the given product 20 by a, number left               20/a
3. The cube of the greater number is                                  aaa
4. The cube of the lesser number is                              8000/aaa
5. Difference of the cubes of the two numbers           (aaaaaa - 8000)/aaa
6. Which difference must equal 61                          (aaaaaa - 8000)/aaa = 61
7. Equation after reduction                                      aaaaaa - 61aaa = 8000
8. Resolving the equation in the last step by the canon                     a = 5
9. When the greater number sought is found 5, the lesser               20/5 = 4.
I say, the numbers 5 and 4 will solve the question proposed.
Kersey also, in parallel, gives the more general solution,
a, b/a, aaa, bbb/aaa, (aaaaaa - bbb)/aaa, (aaaaaa - bbb)/aaa = d, aaaaaa - daaa = bbb, ...
Despite the difficulty that Kersey had in getting his book published, it sold well as Collins confirmed in 1676. Writing a biographical history almost 100 years later, James Granger wrote that Kersey's book was highly regarded [6]:-
John Kersey, teacher of the mathematics, was author of "The Elements of mathematical Art, commonly called Algebra." This book was allowed, by all judges of its merit, to be the clearest, and most comprehensive system of the kind, extant in any language. Very honourable mention is made of it in the "Philosophical Transactions." The work was very much encouraged by Mr John Collins, commonly called attorney-general to the mathematics. Our author, Kersey, published an improved edition of Wingate's "Arithmetic."
Kersey suffered ill health for many years, probably caused by a stone in the bladder. He died in May 1677 and was buried at St Paul, Covent Garden, on 23 May 1677.

Kersey's son, John Kersey, born 1657, became a publisher and worked in partnership with Henry Faithorne at The Rose in St Paul's Churchyard from 1681 to 1686. He revised and made additions to several books that he published, for example the sixth edition of Edward Phillips' The new world of words: or, universal English dictionary. The fourteenth edition of Wingate's Arithmetique was published in 1720 with a note the it was:-
... now exactly corrected by John Kersey, the last author's son.

References (show)

  1. K Barrett, Looking for Longitude: A Cultural History (Liverpool University Press, Liverpool, 2022).
  2. P Beeley and C J Scriba, The Correspondence of John Wallis (1616-1703) (4 Volumes) (Oxford University Press, Oxford, 2008-2014).
  3. J Bibby, John Kersey, Personal Communication (18 July 2023).
  4. J N Brewer, The Beauties of England and Wales: or, Original Delineations, Topographical, Historical, and Descriptive, of each County XII (ii) (Longman & Co., London, 1812).
  5. C Cowman and M O Reilly, Kersey, Mathematics at the Edward Worth Library.
  6. J Granger, A Biographical History of England, from Egbert the Great to the Revolution (T Davies, 1769).
  7. Iohn Kersey borne at bodicot neere Banbvry in the Covnty of Oxford, A.O D.NI 1616, Antique Prints & Maps, Sanders of Oxford.
  8. John Kersey, 1616 - 1677. Mathematician, National Galleries Scotland.
  9. John Kersey, National Portrait Gallery.
  10. John Kersey, mathematician, published 1673 after painting of 1672, Royal Collection Trust.
  11. J Kersey, The elements of that mathematical art commonly called algebra, expounded in four books (William Godbid, London, 1673-74).
  12. Kersey or Carsaye family,
  13. Kersey, John, Dictionary of National Biography
  14. F Cajori, On the invention of the slide rule, Nature 82 2096 (1909), 267-268.
  15. Portrait of John Kersey the elder (1616-1677), Royal Society Print Shop.
  16. S P Rigaud and S J Rigaud (eds.), Correspondence of scientific men of the seventeenth century (2 volumes) (Oxford University Press, Oxford, 1841).
  17. F J Swetz, Mathematical Treasure: John Kersey's Algebra, Convergence, Mathematical Association of America (July 2018).
  18. E G R Taylor, The mathematical practitioners of Tudor and Stuart England (Institute of Navigation at the University Press, 1954).
  19. R Wallis, Kersey, John, the elder (bap. 1616, d. 1677), mathematician, Dictionary of National Biography (Oxford University Press, Oxford, 2004).
  20. E Wingate and J Kersey, Mr Wingate's Arithmetick (1883).

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update September 2023