Roger Cotes

Infobox Scientist
name = Roger Cotes
box_width = 300px

|250px
image_width = 250px
caption = This bust was commissioned by Robert Smith and sculpted posthumously by P. Scheemakers in 1758.
birth_date = birth date|1682|07|10
birth_place = Burbage, Leicestershire, England
death_date = death date and age|1716|06|05|1682|07|10
death_place = Cambridge, Cambridgeshire, England
residence = UK
citizenship =
nationality = British
ethnicity =
field = Mathematician
work_institutions = University of Cambridge
alma_mater = University of Cambridge
doctoral_advisor =
academic_advisors = Isaac Newton
doctoral_students =
notable_students = Robert Smith
James Jurin [Rusnock (2004) " [http://www.oxforddnb.com/view/article/15173 Jurin, James (bap. 1684, d. 1750)] ", "Oxford Dictionary of National Biography", Oxford University Press, accessed 6 September 2007 ODNBsub]
Stephen Gray
known_for = Logarithmic spiral
Least squares
Newton–Cotes formulas
Euler's formula proof
Concept of the radian
author_abbrev_bot =
author_abbrev_zoo =
influences = John Smith (his uncle) Gowing, Ronald, "Roger Cotes - Natural Philosopher", Cambridge University Press, 2002, p. 6. ]
influenced =
prizes =
religion =
footnotes =

Roger Cotes FRS (July 10, 1682 – June 5, 1716) was an English mathematician, known for working closely with Isaac Newton by proofreading the second edition of his famous book, the "Principia", before publication. He also invented the quadrature formulas known as Newton–Cotes formulas and first introduced what is known today as Euler's formula. He was the first Plumian Professor at Cambridge University from 1707 until his death.

Early life

Cotes was born in Burbage, Leicestershire. His parents were Robert, the rector of Burbage, and his wife Grace "née" Farmer. Roger had an elder brother, Anthony (born 1681) and a younger sister, Susanna (born 1683). At first Roger attended Leicester School where his mathematical talent was recognised. His aunt Hannah had married Rev. John Smith, and Smith took on the role of tutor to encourage Roger's talent. The Smiths' son, Robert Smith, would become a close associate of Roger Cotes throughout his life. Cotes later studied at St Paul's School in London and then at Trinity College, Cambridge. He graduated BA in 1702 and MA in 1706.Meli (2004)]

Astronomy

Roger Cotes's contributions to modern computational methods lie heavily in the fields of astronomy and mathematics. Cotes began his educational career with a focus on astronomy. He became a fellow of Trinity College in 1707, and at age 26 he became the first Plumian Professor of Astronomy and Experimental Philosophy. On his appointment to professor, he opened a subscription list in an effort to provide an observatory for Trinity. Unfortunately, the observatory still was unfinished when Cotes died, and was demolished in 1797.

In correspondence with Isaac Newton, Cotes designed a heliostat telescope with a mirror revolving by clockwork.Fact|date=September 2007 He recomputed the solar and planetary tables of Giovanni Domenico Cassini and John Flamsteed, and he intended to create tables of the moon's motion, based on Newtonian principles.Fact|date=September 2007 Finally, in 1707 he formed a school of physical sciences at Trinity in partnership with William Whiston.

The "Principia"

From 1709 to 1713, Cotes became heavily involved with the second edition of Newton's "Principia", a book that explained Newton's theory of universal gravitation. The first edition of "Principia" had only a few copies printed and was in need of revision to include Newton's works and principles of lunar and planetary theory. Newton at first had a casual approach to the revision, since he had all but given up scientific work.Fact|date=September 2007 However, through the vigorous passion displayed by Cotes, Newton's scientific hunger was once again reignited.Fact|date=September 2007 The two spent nearly three and half years collaborating on the work, in which they fully deduce, from Newton's laws of motion, the theory of the moon, the equinoxes, and the orbits of comets. Only 750 copies of the second edition were printed. However, a pirate copy from Amsterdam met all other demand.Fact|date=September 2007 As reward to Cotes, he was given a share of the profits and 12 copies of his own.Fact|date=September 2007 Cotes's original contribution to the work was a preface which supported the scientific superiority of Newton's principles over the then popular vortex theory of gravity advocated by René Descartes. Cotes concluded that the Newton's law of gravitation was confirmed by observation of celestial phenomenon that were inconsistent with the vortex phenomena that Cartesian critics alleged.

Mathematics

Cotes's major original work was in mathematics, especially in the fields of integral calculus, logarithms, and numerical analysis. He published only one scientific paper in his lifetime, entitled "Logometrica", in which he successfully constructs the logarithmic spiral.O'Connor & Robertson (2005)] After his death, many of Cotes's mathematical papers were hastily edited by Robert Smith and published in a book, "Harmonia mensurarum". Cotes's additional works were later published in Thomas Simpson's "The Doctrine and Application of Fluxions". Although Cotes's style was somewhat obscure, his systematic approach to integration and mathematical theory was highly regarded by his peers.Fact|date=September 2007 Cotes discovered an important theorem on the nth roots of unity, foresaw the method of least squares, and he discovered a method for integrating rational fractions with binomial denominators. He was also praised for his efforts in numerical methods, especially in interpolation methods and his table construction techniques. He was regarded as one of the few British mathematicians capable of following the powerful work of Sir Isaac Newton.Fact|date=September 2007

Death and assessment

Cotes died from a violent fever in Cambridge in 1716 at the early age of 33. Isaac Newton remarked, "If he had lived we would have known something."

References

Bibliography

* [Anon.] (1911) " [http://www.1911encyclopedia.org/Roger_Cotes Roger Cotes] , "Encyclopaedia Britannica"
* cite book | author=Cohen, I. B. | title=Introduction to Newton’s "Principia" | year=1971 | id=ISBN 0674461932 | publisher=Harvard University Press | location=Harvard
* cite book | title=Correspondence of Sir Isaac Newton and Professor Cotes | author=Edleston, J. (ed.) | year=1850
* cite book | author=Gowing, R. | title=Roger Cotes: Natural Philosopher | year=2002 | id=ISBN 0521526493 | location=London | publisher=Cambridge University Press
* cite book | author=Koyré, A. | title=Newtonian Studies | year=1965 | pages=273–82 | id=ISBN 0412423006 | location=London | publisher=Chapman & Hall
*Meli, D. B. (2004) " [http://www.oxforddnb.com/view/article/6386 Cotes, Roger (1682–1716)] ", "Oxford Dictionary of National Biography", Oxford University Press, accessed 7 September 2007 ODNBsub
*MacTutor|id=Cotes (2005)
* cite journal | author=Price, D. J. | title=The early observatory instruments of Trinity College, Cambridge | journal=Annals of Science | volume=8 | year=1952 | pages=1–12 | doi=10.1080/00033795200200012
* cite book | title=The Correspondence of Isaac Newton | author=Turnbull, H. W. "et al." | edition=7 vols | pages=vols.5–6 | year=1975–6 | location=London | publisher=Cambridge University Press
* cite book | title=Isaac Newton's Philosophiae Naturalis Principia Mathematica: The Third Edition (1726) with Variant Readings | author=Whitman, A. "et al." (eds) | year=1972 | pages=817–26 | id=ISBN 0521079608 | location=London | publisher=Cambridge University Press

External links

* web cite | url=http://www.mathpages.com/home/kmath192/kmath192.htm | title="Harmonia Mensurarum" | work=MathPages | accessdate=2007-09-07 - A more complete account of Cotes's involvement with "Principia", followed by an even more thorough discussion of his mathematical work.