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27-958: James Gregory may refer to: James Gregory (mathematician) (1638–1675), Scottish mathematician and astronomer James Gregory (physician) (1753–1821), Scottish physician James J. H. Gregory (1827–1910), American educator, businessman, writer, politician, and philanthropist James Gregory (mineralogist) (1832–1899), Scottish mineralogist James Gregory (actor) (1911–2002), American actor James Gregory (prison officer) (1941–2003), South African prison guard, author of Goodbye Bafana James Gregory (comedian) (1946-2024), American comedian Jim Gregory (basketball) , American former college basketball standout Jim Gregory (football chairman) (1928–1998), former English football club director and chairman Jim Gregory (footballer) (1876–1949), Australian rules footballer Jim Gregory (ice hockey) (1935–2019), Canadian general manager and league executive in

54-516: A "Gregorian dome". The following excerpt is from the Pantologia . A new (cabinet) cyclopædia (1813) Mr. James Gregory was a man of a very acute and penetrating genius. ...The most brilliant part of his character was that of his mathematical genius as an inventor, which was of the first order; as will appear by... his inventions and discoveries [which include] quadrature of the circle and hyperbola, by an infinite converging series; his method for

81-411: A circle from the tangent, and vice versa; as also for the secant and logarithmic tangent and secant, and vice versa. These, with others, for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some received from him of Newton's , in which he followed the elegant example of this author, in delivering his series in simple terms, independent of each other. In

108-464: A letter of 1671 to John Collins , Gregory gives the power series expansion of the seven functions (using modern notation) arctan ⁡ x {\textstyle \arctan x} (often called Gregory's series ), tan ⁡ x , {\textstyle \tan x,} sec ⁡ x , {\textstyle \sec x,} log sec ⁡ x , {\textstyle \log \,\sec x,}

135-514: A physician and inventor. About a year after assuming the Chair of Mathematics at Edinburgh , James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36. In the Optica Promota , published in 1663, Gregory described his design for a reflecting telescope , the " Gregorian telescope ". He also described the method for using

162-565: A reflecting telescope with a parabolic mirror would correct spherical aberration as well as the chromatic aberration seen in refracting telescopes . In his design he also placed a concave secondary mirror with an elliptical surface past the focal point of the parabolic primary mirror , reflecting the image back through a hole in the primary mirror where it could be conveniently viewed. According to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one. The telescope design attracted

189-408: Is different from Wikidata All article disambiguation pages All disambiguation pages James Gregory (mathematician) In his book Geometriae Pars Universalis (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of

216-460: Is unsuitable for irregular surfaces, and Gregory devised an appropriate "adaptable wheel" using a Gregory transformation . Gregory, an enthusiastic supporter of Newton, later had much friendly correspondence with him and incorporated his ideas into his own teaching, ideas which at that time were controversial and considered quite revolutionary. The crater Gregory on the Moon is named after him. He

243-484: The continent , and was a professor of mathematics in Paris by the start of the seventeenth century. There he published or edited, between the years 1612 and 1619, various geometric and algebraic tracts. He described himself as having "more wisdom than riches" in the dedication of Vindiciae Archimedis (1616). He was first cousin of David Anderson of Finshaugh, a celebrated mathematician, and David Anderson's daughter

270-554: The fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him." The book was reprinted in 1668 with an appendix, Geometriae Pars , in which Gregory explained how the volumes of solids of revolution could be determined. In his 1663 Optica Promota , James Gregory described his reflecting telescope which has come to be known by his name, the Gregorian telescope. Gregory pointed out that

297-576: The transit of Venus to measure the distance of the Earth from the Sun, which was later advocated by Edmund Halley and adopted as the basis of the first effective measurement of the Astronomical Unit . Before he left Padua, Gregory published Vera Circuli et Hyperbolae Quadratura (1667) in which he approximated the areas of the circle and hyperbola with convergent series: "The first proof of

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324-526: The Gudermannian function 2 arctan ⁡ e x − 1 2 π . {\textstyle 2\arctan e^{x}-{\tfrac {1}{2}}\pi .} There is evidence that he discovered the method of taking higher derivatives in order to compute a power series, which was not discovered by Taylor until 1715, but did not publish his results, thinking he had only rediscovered "Mr. Newton's universal method," which

351-578: The National Hockey League Jim Gregory (politician) (elected 2018), American politician from Pennsylvania James Crawford Gregory (1801–1832), Scottish physician James G. Gregory (1843–1932), Surgeon General of Connecticut and member of the Connecticut House of Representatives James Monroe Gregory (1849–1915), professor of Latin and dean at Howard University [REDACTED] Topics referred to by

378-593: The attention of several people in the scientific establishment such as Robert Hooke , the Oxford physicist who eventually built the telescope 10 years later, and Sir Robert Moray , polymath and founding member of the Royal Society . The Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are also used in radio telescopes such as Arecibo , which features

405-546: The first Regius Professor of Mathematics at the University of St Andrews , a position created for him by Charles II , probably upon the request of Robert Moray. There at the University of St Andrews , he laid the first meridian line across the floor of his lab in 1673, which was 200 years prior to the Greenwich Meridian being established, and thus "arguably making St Andrews the place where time began". He

432-592: The founders of the Royal Society . In 1664 he departed for the University of Padua , in the Venetian Republic , passing through Flanders , Paris and Rome on his way. At Padua he lived in the house of his countryman James Caddenhead , the professor of philosophy, and he was taught by Stefano Angeli . Upon his return to London in 1668 he was elected a Fellow of the Royal Society , before travelling to St Andrews in late 1668 to take up his post as

459-445: The inverse Gudermannian function log tan ⁡ 1 2 ( x + 1 2 π ) {\textstyle \log \,\tan {\tfrac {1}{2}}{\bigl (}x+{\tfrac {1}{2}}\pi {\bigr )}} , arcsec ⁡ ( 2 e x ) , {\textstyle \operatorname {arcsec} {\bigl (}{\sqrt {2}}e^{x}{\bigr )},} and

486-477: The last of them was published in 1619, it is probable that the author died soon after that year, but the precise date is unknown. He wrote other works that have since been lost. From his last work it appears he wrote another piece, "A Treatise on the Mensuration of Solids," and copies of two other works, Ex. Math. and Stereometria Triangulorum Sphæricorum , were in the possession of Sir Alexander Hume until

513-407: The same term This disambiguation page lists articles about people with the same name. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=James_Gregory&oldid=1259735303 " Category : Human name disambiguation pages Hidden categories: Short description

540-406: The solution of the famous Keplerian problem by an infinite series; he discovered a method of drawing Tangents to curves geometrically, without any previous calculations; a rule for the direct and inverse method of tangents, which stands upon the same principle (of exhaustions ) with that of fluxions , and differs not much from it in the manner of application; a series for the length of the arc of

567-431: The theorem), for which he was acknowledged by Isaac Barrow . Gregory was born in 1638. His mother Janet was the daughter of Jean and David Anderson and his father was John Gregory, an Episcopalian Church of Scotland minister , James was youngest of their three children and he was born in the manse at Drumoak , Aberdeenshire , and was initially educated at home by his mother, Janet Anderson (~1600–1668). It

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594-401: The transformation of curves; a geometrical demonstration of Lord Brouncker's series for squaring the hyperbola—his demonstration that the meridian line is analogous to a scale of logarithmic tangents of the half complements of the latitude; he also invented and demonstrated geometrically, by help of the hyperbola, a very simple converging series for making the logarithms; he sent to Mr. Collins

621-400: Was based on a different technique. James Gregory discovered the diffraction grating by passing sunlight through a bird feather and observing the diffraction pattern produced. In particular he observed the splitting of sunlight into its component colours – this occurred a year after Newton had done the same with a prism and the phenomenon was still highly controversial. A round wheel

648-479: Was his mother who endowed Gregory with his appetite for geometry , her uncle – Alexander Anderson (1582–1619) – having been a pupil and editor of French mathematician Viète . After his father's death in 1651 his elder brother David took over responsibility for his education. He attended Aberdeen Grammar School , and then Marischal College from 1653–1657, graduating AM in 1657. In 1663 he went to London, meeting John Collins and fellow Scot Robert Moray , one of

675-409: Was successively professor at the University of St Andrews and the University of Edinburgh . He had married Mary, daughter of George Jameson , painter, and widow of John Burnet of Elrick, Aberdeen; their son James was Professor of Physics at King's College, Aberdeen . He was the grandfather of John Gregory (FRS 1756); uncle of David Gregorie (FRS 1692) and brother of David Gregory (1627–1720),

702-531: Was the mother of mathematician James Gregory . He was selected by the executors of François Viète to revise and edit Viète's manuscript works. Viète died in 1603, and it is unclear if Anderson knew him, but his eminence was sufficient to attract the attention of the dead man's executors. Anderson corrected and expanded upon Viète's manuscripts, which extended known geometry to the new algebra , which used general symbols to represent quantities. The known works of Anderson amount to six thin quarto volumes, and as

729-613: Was the uncle of mathematician David Gregory . Alexander Anderson (mathematician) Alexander Anderson ( c.  1582 in Aberdeen – c.  1620 in Paris ) was a Scottish mathematician . He was born in Aberdeen , possibly in 1582, according to a print which suggests he was aged 35 in 1617. It is unknown where he was educated, but it is likely that he initially studied writing and philosophy (the "belles lettres") in his home city of Aberdeen. He then went to

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