Information about Roger Cotes

Roger Cotes

Roger Cotes (1682-1716).
Born	July 10, 1682 Burbage, Leicestershire
Died	June 5, 1716 Cambridge, Cambridgeshire
Residence	UK
Nationality	British
Field	Mathematician
Institutions	Cambridge University
Alma mater	Cambridge University
Academic advisor	Isaac Newton
Notable students	Robert Smith James Jurin
Known for	Logarithmic spiral Least squares

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 he attended Leicester School where his mathematical talent was recognised. Roger's aunt Hannah had married Rev. John Smith and Smith took on the role of tutor to encourage Roger's talent. The Smith's son, Robert Smith would become a close associate of Roger 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.^[1]

Astronomy

Roger Cotes's contributions to modern computational methods lie heavily in the fields of astronomy and mathematics. Cotes began his professional educational career with a particular 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 was never finished in Cotes's lifetime and was demolished in 1797.^[1] Astronomy continued to fascinate Cotes. In correspondence with Isaac Newton, he designed a heliostat telescope with a mirror revolving by clockwork. 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. Finally, in 1707 he formed a school of physical sciences at Trinity in partnership with William Whiston.^[1]

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.^[1] Newton at first had a casual approach to the revision, since he had all but given up scientific work. However, through the vigorous passion displayed by Cotes, Newton's scientific hunger was once again reignited. 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.^[1] However, a pirate copy from Amsterdam met all other demand. As reward to Cotes, he was given a share of the profits and 12 copies of his own. 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.^[1]

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.^[2] After his death, many of Cotes's mathematical papers were hastily edited by Robert Smith and published in a book, Harmonia mensurarum.^[1] Cotes's additional works were later published in Thomas Simpson's The Doctrine and Application of Fluxions.^[2] Although Cotes's style was somewhat obscure, his systematic approach to integration and mathematical theory was highly regarded by his peers. Cotes had 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.^[2] He was also praised for his efforts in numerical methods, especially in interpolation methods and his table construction techniques.^[2] He was regarded as one of the few British mathematicians capable of following the powerful work of Sir Isaac Newton.

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."^[1]

References

Bibliography

• [Anon.] (1911) "Roger Cotes, Encyclopaedia Britannica
• Cohen, I. B. (1971). Introduction to Newton’s "Principia". Harvard: Harvard University Press. ISBN 0674461932. 
• Edleston, J. (ed.) (1850). Correspondence of Sir Isaac Newton and Professor Cotes. 
• Gowing, R. (2002). Roger Cotes: Natural Philosopher. London: Cambridge University Press. ISBN 0521526493. 
• Koyré, A. (1965). Newtonian Studies. London: Chapman & Hall, 273–82. ISBN 0412423006. 
• Meli, D. B. (2004) "Cotes, Roger (1682–1716)", Oxford Dictionary of National Biography, Oxford University Press, accessed 7 September 2007 (subscription or UK/ Ireland public library membership required)
• O'Connor, John J; Edmund F. Robertson "Roger Cotes". MacTutor History of Mathematics archive.   (2005)
• Price, D. J. (1952). "The early observatory instruments of Trinity College, Cambridge". Annals of Science 8: 1–12. 
• Turnbull, H. W. et al. (1975–6). The Correspondence of Isaac Newton, 7 vols, London: Cambridge University Press, vols.5–6. 
• Whitman, A. et al. (eds) (1972). Isaac Newton's Philosophiae Naturalis Principia Mathematica: The Third Edition (1726) with Variant Readings. London: Cambridge University Press, 817–26. ISBN 0521079608. 

External links

• Harmonia Mensurarum. MathPages. Retrieved on 2007-09-07., a more complete account of Cotes's involvement with Principia, followed by an even more thorough discussion of his mathematical work.

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Academic Genealogy
Notable teachers	Notable students
Isaac Newton	Robert Smith[1] James Jurin[3]