Roger Cotes: Perbedaan antara revisi

Dalam korespondensi dengan Isaac Newton, Cotes merancang teleskop [[heliostat]] dengan cermin yang berputar dengan jarum jam.<ref>Edleston, J., ed. (1850) ''Correspondence of Sir Isaac Newton and Professor Cotes, …'' (London, England: John W. Parker), [https://archive.org/stream/correspondenceof00newtrich#page/197/mode/2up "Letter XCVIII. Cotes to John Smith."] (1708 February 10), pp. 197–200.</ref><ref>{{Cite web|last=Kaw|first=Autar|date=2003-01-01|title=cotes - A Historical Anecdote|url=http://mathforcollege.com/nm/anecdotes/cotes.html|website=mathforcollege.com|access-date=2017-12-12}}</ref> Dia menghitung ulang tabel matahari dan planet buatan [[Giovanni Domenico Cassini]] dan [[John Flamsteed]], dan dia berniat membuat tabel [[Orbit|pergerakan]] [[bulan]] berdasarkan prinsip Newton.  Akhirnya, pada tahun 1707 ia membentuk sekolah ilmu fisika di Trinity dalam kemitraan dengan [[William Whiston]].<ref name="ODNB">Meli (2004)</ref>

Karya asli utama Cotes adalah dalam matematika, terutama di bidang [[Integral|kalkulus integral]], [[logaritma]], dan [[analisis numerik]]. Dia hanya menerbitkan satu [[Karya Tulis Ilmiah|makalah ilmiah]] dalam hidupnya, berjudul ''Logometria'', di mana dia berhasil membangun [[spiral logaritmik]].<ref name="mactutor">O'Connor & Robertson (2005)</ref><ref>In ''Logometria'', Cotes evaluated [[E (mathematical constant)|e, the base of natural logarithms]], to 12 decimal places. See: Roger Cotes (1714) "Logometria," ''Philosophical Transactions of the Royal Society of London'', '''29''' (338) : 5-45; [http://babel.hathitrust.org/cgi/pt?id=ucm.5324351035;view=2up;seq=16 see especially the bottom of page 10.] From page 10: ''"Porro eadem ratio est inter 2,718281828459 &c et 1, … "'' (Furthermore, the same ratio is between 2.718281828459… and 1, … )</ref> Setelah kematiannya, banyak makalah matematika Cotes yang diedit oleh sepupunya Robert Smith dan diterbitkan dalam sebuah buku, ''Harmonia mensurarum''.<ref name="ODNB">Meli (2004)</ref><ref>''Harmonia mensurarum'' contains a chapter of comments on Cotes' work by Robert Smith. On page 95, Smith gives the value of 1 [[radian]] for the first time. See: Roger Cotes with Robert Smith, ed., ''Harmonia mensurarum'' … (Cambridge, England: 1722), chapter: Editoris notæ ad Harmoniam mensurarum, [https://books.google.com/books?id=J6BGAAAAcAAJ&pg=RA1-PA95#v=onepage&q&f=false top of page 95]. From page 95: After stating that 180° corresponds to a length of π (3.14159…) along a unit circle (i.e., π radians), Smith writes: ''"Unde Modulus Canonis Trigonometrici prodibit 57.2957795130 &c. "'' (Whence the conversion factor of trigonometric measure, 57.2957795130… [degrees per radian], will appear.)</ref> Karya tambahan Cotes kemudian diterbitkan dalam ''The Doctrine and Application of Fluxions'' karya [[Thomas Simpson]].<ref name="mactutor" /> Meskipun gaya penulisan dan penjelasan Cotes tidak terlalu jelas, pendekatan sistematisnya terhadap [[Integral|integrasi]] dan teori matematika sangat dihargai oleh rekan-rekannya.{{Butuh rujukan|date=September 2007}} Cotes menemukan teorema penting pada [[akar persatuan]] ke-''n'',<ref>Roger Cotes with Robert Smith, ed., ''Harmonia mensurarum'' … (Cambridge, England: 1722), chapter: "Theoremata tum logometrica tum triogonometrica datarum fluxionum fluentes exhibentia, per methodum mensurarum ulterius extensam" (Theorems, some logorithmic, some trigonometric, which yield the fluents of given fluxions by the method of measures further developed), [https://books.google.com/books?id=J6BGAAAAcAAJ&pg=PA113#v=onepage&q&f=false pages 113-114.]</ref> meramalkan metode [[kuadrat terkecil]],<ref>Roger Cotes with Robert Smith, ed., ''Harmonia mensurarum'' … (Cambridge, England: 1722), chapter: "Aestimatio errorum in mixta mathesis per variationes partium trianguli plani et sphaerici" Harmonia mensurarum ..., pages 1-22, see especially [https://books.google.com/books?id=J6BGAAAAcAAJ&pg=RA1-PA20#v=onepage&q&f=false page 22.] From page 22: ''"Sit p locus Objecti alicujus ex Observatione prima definitus, … ejus loco tutissime haberi potest."'' (Let p be the location of some object defined by observation, q, r, s, the locations of the same object from subsequent observations. Let there also be weights P, Q, R, S reciprocally proportional to the displacements that may arise from the errors in the single observations, and that are given from the given limits of error; and the weights P, Q, R, S are conceived as being placed at p, q, r, s, and their center of gravity Z is found: I say the point Z is the most probable location of the object, and may be most safely had for its true place. [Ronald Gowing, 1983, p. 107])</ref> dan menemukan metode untuk mengintegrasikan [[pecahan rasional]] dengan [[Pecahan|penyebut]] [[Binomial (polinomial)|binomial]] <ref name="mactutor" /> <ref>Cotes presented his method in a letter to William Jones, dated 5 May 1716. An excerpt from the letter which discusses the method was published in: [Anon.] (1722), Book review: "An account of a book, intitled, ''Harmonia Mensurarum'', … ," ''Philosophical Transactions of the Royal Society of London'', '''32''' : 139-150 ; see [http://babel.hathitrust.org/cgi/pt?id=ucm.5324350998;view=2up;seq=166 pages 146-148.]</ref> Dia juga dipuji atas usahanya dalam metode numerik, terutama dalam metode [[Interpolasi (matematika)|interpolasi]] dan teknik konstruksi tabelny. <ref name="mactutor" /> Dia dianggap sebagai salah satu dari sedikit matematikawan Inggris yang mampu mengikuti karya hebat Sir Isaac Newton.{{Butuh rujukan|date=September 2007}}

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