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Source: https://mathshistory.st-andrews.ac.uk/Biographies/Cotes/
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MacTutorRoger Cotes
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Burbage, Leicestershire, England
Cambridge, England
Biography
Roger Cotes' mother was Grace Farmer, who came from Barwell in Leicestershire, and his father was Robert Cotes who was the rector of Burbage. Roger had a brother Anthony one year older than himself, and a sister Susanna who was one year younger. He attended Leicester School and by the age of twelve his teachers had already realised that he had an exceptional mathematical talent. His uncle, the Reverend John Smith, was keen to give Roger every chance to develop these talents and so Roger went to live with him so that he might be personally tutored. Roger later attended the famous St Paul's School in London, but he continued to be advised by his uncle and the two exchanged letters on mathematical topics during the time that Roger spent at school in London.Roger matriculated at Trinity College, Cambridge, on 6 April 1699 as a pensioner, meaning that he did not have a scholarship and paid for his own keep in College. He graduated with a B.A. in 1702 and remained at Cambridge where he was elected to a fellowship in 1705. In January 1706 he was nominated to be the first Plumian Professor of Astronomy and Experimental Philosophy. This was a remarkable achievement for Cotes who, at that time, was on 23 years of age. His exceptional abilities had been fully appreciated, however, by many at Cambridge such as William Whiston with whom he had quickly formed a friendship. Both Newton and Whiston recommended Cotes for the Chair, as did Richard Bentley who was master of Trinity College. There were some, however, who opposed his appointment, the most high profile of whom was Flamsteed, the astronomer royal. By the time that Cotes was formally elected as Plumian Professor on 16 October 1707 he had, in the previous year, been elected to a more prestigious fellowship as well as being awarded his M.A. Meli gives the background to the establishment of the chair in [2]:-
Cotes was the first occupant of the Cambridge chair established by Thomas Plume (1630 - 1704), archdeacon of Rochester, who bequeathed nearly £2000 to maintain a professor and erect an astronomical observatory. Plans for an observatory at Trinity had already been drafted by Bentley before Plume's bequest. The observatory was eventually housed over the king's or great gate at Trinity College, together with living quarters for the Plumian professor.It is not entirely clear how successful Cotes was in his role as an observational astronomer. In the first place there are somewhat contradictory accounts of the quality of the instruments in the Cambridge observatory. Cotes designed a transit telescope to add to a collection of instruments which had been purchased or donated. For example Newton donated a clock which still survives at Trinity College. Bentley, the master of Trinity College we mentioned above, claimed that the Observatory had "the best instruments in Europe" but an assistant who worked there wrote to Flamsteed saying "I saw nothing there that might deserve your notice". The truth is probably somewhere in between, since it would be natural for the master of Trinity to boast of the facilities, while the assistant, who only worked there for a short time, was probably trying to please Flamsteed. In terms of the observations that Cotes made, perhaps the most significant was the total eclipse on 22 April 1715. However, Halley describes this event in a paper in the Philosophical Transactions of the Royal Society where he says that Cotes:-
... had the misfortune to be opprest by too much company, so that though the heavens were very favourable, yet he missed both the times of the beginning of the eclipse and that of total darkness.Cotes himself wrote a letter to Newton concerning the eclipse in which he explained that his assistant had discovered a method to determine the mid-point of the ec