Roger Cotes (Burbage, Leicestershire July 10, 1682 – June 5, 1716 in Cambridge, Cambridgeshire) was an English mathematician. Burbage is a parish in Leicestershire in the United Kingdom. ... July 10 is the 191st day (192nd in leap years) of the year in the Gregorian Calendar, with 174 days remaining. ... Events March 11 – Chelsea hospital for soldiers is founded in England May 6 - Louis XIV of France moves his court to Versailles. ... June 5 is the 156th day of the year in the Gregorian calendar (157th in leap years), with 209 days remaining. ... // Events August 5 - In the Battle of Peterwardein 40. ... Shown within Cambridgeshire Geography Status City (1951) Region East of England Admin. ... Cambridgeshire (abbreviated Cambs) is a county in England, bordering Lincolnshire to the north, Norfolk to the northeast, Suffolk to the east, Essex and Hertfordshire to the south, and Bedfordshire and Northamptonshire to the west. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

Roger Cotes is known for working closely with Isaac Newton by proofreading the second edition of his famous book 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. Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, widely regarded as one of the key figures in the history of science. ... Newtons own copy of his Principia, with hand written corrections for the second edition. ... In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe numerical algorithms for solving differential equations. ... In numerical analysis, the Newton-Cotes formulas, also called the Newton-Cotes rules, are a group of formulas for numerical integration (also called quadrature) based on evaluating the integrand at n+1 equally-spaced points. ... Eulers formula, named after Leonhard Euler, is a mathematical formula in complex analysis that shows a deep relationship between the trigonometric functions and the complex exponential function. ... The Plumian chair of Astronomy and Experimental Philosophy is one of the two major Professorships in Astronomy at Cambridge University, alongside the Lowndean Professorship. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ...

Roger Cotes accomplishments and life can be summed up as a great case of might have been. Cotes 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 the Trinity College of Cambridge 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 lifetime and was demolished in 1797. Astronomy continued to fascinate Cotes, driving him to, in correspondence with Isaac Newton, to design a heliostat telescope with a mirror revolving by clockwork. He recomputed the solar and planetary tables of J.D. Cassini and 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. A giant Hubble mosaic of the Crab Nebula. ... MolÄ—tai Astronomical Observatory An observatory is a location used for observing terrestrial and/or celestial events. ... William Whiston William Whiston (December 9, 1667 - August 22, 1752), English divine and mathematician, was born at Norton in Leicestershire, of which village his father was rector. ...

From 1709 to 1713, Cotes became heavily involved with the second edition of Newton's Principia, a book that explained Newton's theories on universal gravitation. Newton's first edition of Principia had only a few copies printed and was in need of updating and 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 gave up scientific work. However, through the vigorous passion displayed by Cotes efforts, 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, through Newton's principles, the theory of the moon and the equinoxes, as well as, the theory of comets and their orbits. The total number of works printed for this addition was limited to 750 copies. 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' original contribution to the work involve a preface with supported the scientific superiority of Newton's principles over the then popular idea of vortices presented by Descartes. Cotes concluded that the Newton's law of gravitation was confirmed by observation of celestial phenomenon and did not depend on unexplained occult forces which Cartesian critics alleged. Bulk composition of the Moons mantle and crust estimated, weight percent Oxygen 42. ... An equinox is one of two opposite points on the celestial sphere where the celestial equator and ecliptic intersect. ... Comet Hale-Bopp For other uses, see Comet (disambiguation). ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... Amsterdam Location Flag Country Netherlands Province North Holland Population 743,905 (1 April 2006) Demonym Amsterdammer Coordinates Website www. ... This is an article on the real vortex phenomena. ... René Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher, mathematician, and scientist. ...

Cotes' major original work was in mathematics, especially in the fields of integration calculus methods, logarithms, and numerical methods. Cotes' published only one paper in his lifetime, entitled Logometrica, in which he successfully constructs the logarithmic curve. After his death, many of Cotes' mathematical papers were hastily edited by Robert Smith and published in Harmonia mensurarum. Cotes additional works were later published in Thomas Simpson's The Doctrine and Application of Fluxions. Although Cotes' style was somewhat obscure, Cotes' 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. Furthermore, Cotes was praised for his efforts in numerical methods, especially in interpolation methods and his table construction techniques. This article deals with the concept of an integral in calculus. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Thomas Simpson (August 20, 1110 – May 14, 1761) was a British mathematician, inventor and eponym of Simpsons rule to approximate definite integrals. ... In mathematics, the nth roots of unity or de Moivre numbers are all the complex numbers which yield 1 when raised to a given power n. ... Least squares is a mathematical optimization technique which, when given a series of measured data, attempts to find a function which closely approximates the data (a best fit). It attempts to minimize the sum of the squares of the ordinate differences (called residuals) between points generated by the function and... In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points. ...

Cotes untimely death from a violent fever, coupled with the added decline in British mathematics as the time, have lead many to remember Cotes as one of the few British mathematicians capable of following the powerful work of Sir Isaac Newton. Cotes' drive and intuition lead Newton to say "If he had lived we would have known something".

External link

• O'Connor, John J., and Edmund F. Robertson. "Roger Cotes". MacTutor History of Mathematics archive.