61. McLaurin And Brooke Taylor Lecture 22 colin maclaurin and Brooke Taylor. Background to the text.colin maclaurin (16981746), Professor of Mathematics in Aberdeen at the age of 19 http://www.maths.uwa.edu.au/~schultz/3M3/L22McLaurin.html

Lecture 22: Colin MacLaurin and Brooke Taylor Background to the text Colin Maclaurin (16981746), Professor of Mathematics in Aberdeen at the age of 19 and in Edinburgh at 25 on the recommendation of Newton, was the foremost British mathematician in the generation following Newton. He did important work in Euclidean geometry, algebraic geometry (properties of curves described by rational functions in two or three variables), and of course series. The Maclaurin series itself had already been published by Brook Taylor, as well as James Gregory, Jean Bernoulli and James Stirling. However Maclaurin's method of obtaining the coefficients was original. Some of his most important work was in solutions of linear systems, including determinants and Cramer's Rule (before Cramer). We now consider his response to Berkeley, for which he wrote his Treatise on Fluxions . This is by far the most satisfactory of many attempts to refute Berkeley in the period 1740-1750. MacLaurin's aim is to demonstrate the validity of Newton's Method of Fluxions by the rigorous mathods of geometry. In fact, he tries to replace all arguments involving infinitesimals by the method of exhaustion. The extract we study concerns the fluxion of A when A is a uniformly flowing point with fluxion a. It relies on a previous section of the treatise in which he had shown

62. TAYLOR,B.(1685-1731) And MACLAURIN,C.(1698-1746) Emery student of the calculus is familiar with the name of the Englishman BrookTaylor (16851731) and the mane of the Scotsman colin maclaurin (1698-1746), http://library.thinkquest.org/22584/temh3022.htm

BACK Index of Development Graphic Version TAYLOR,B.(1685-1731) and MACLAURIN,C.(1698-1746) Emery student of the calculus is familiar with the name of the Englishman Brook Taylor (1685-1731) and the mane of the Scotsman Colin Maclaurin (1698-1746), through the very useful Taylor's expansion and Maclaurin's ex pansion of a function. It was in 1715 that Taylor published (with no consider ation of convergence) his well-known expansion theorem. In 1717, Thaylor applied his series to the solution of numerical equations as follows: Let a be an approximation to a root of f (¥ö) = 0; set f (a)= k f (a)= k , and ¥ö= a h ; expand = f a h )by the series; discard all powers of h above the second; substitute the values of k k k , and then solve for h . By successive applications of this process, closer and colser approximations can be obtained. Some work done by Taylor in the theory of perspectiove has found a modern application in the mathematical treatment of photogrammetry, the science of surveying by means of photographs taken from an airplane. Recognition of the full importance of Taylor's series awaited until 1755, when Euler applied them in his differntial calculus, and still later, when La grange used the series whith a remainder as the foundation of his theory of functions.

63. Å×ÀÏ·¯(Brook Taylor, 1685-1731)¿Í ¸ÅŬ·Î¸°(Colin Maclaurin, 1698 Translate this page The summary for this Korean page contains characters that cannot be correctly displayed in this language/character set. http://library.thinkquest.org/22584/tmh3022.htm

BACK Index of Development Graphic Version Å×ÀÏ·¯(Brook Taylor, 1685-1731)¿Í ¸ÅŬ·Î¸°(Colin Maclaurin, 1698-1746) ¹ÌÀûºÐÀ» °øºÎÇÏ´Â ÇлýµéÀº ¸Å¿ì À¯¿ëÇÑ ÇÔ¼öÀÇ ÄÉÀÏ·¯ Àü°³¿Í ¸ÅŬ·Î¸° Àü°³À» ÅëÇÏ¿© ¿µ±¹ÀÇ ¼öÇÐÀÚ Å×ÀÏ·¯(Brook Taylor. 1685-1731)¿Í ½ºÄÚƲ·£µå ¼öÇÐ ¸ÅÅ©·Î¸°(Colin Maclaurin, 1698-1746)ÀÇ À̸§À» Àß ¾Ë°í ÀÖ´Ù. Å×ÀÏ·¯°¡ (¼ö·É¼ºÀÇ °íÂû ¾øÀÌ)Àß ¾Ë·ÁÁø Àü°³ Á¤¸® 1717³â¿¡ Å×ÀÏ·¯´Â ´ÙÀ½°ú °°ÀÌ ¼öÄ¡ ¹æÁ¤½ÄÀÇ ÇØ¿¡ ±×ÀÇ ±Þ¼ö¸¦ Àû¿ëÇÏ¿´´Ù. "a¸¦ f(x)=0ÀÇ ±ÙÀÇ ±Ù»ç°ªÀ̶ó°í ÇÏ°í f(a)=k , f'(a)=k', f"(a)=k", x=a+b¶ó ³õÀÚ. 0=f(a+b) ¸¦ ±Þ¼ö Àü°³ÇÏ¿© bÀÇ 2Â÷ ÀÌ»óÀÇ Ç×À» ¹«½ÇÏ°í k, k', k"ÀÇ °ªÀ» ´ëÀÔÇϸé b¸¦ ±¸ÇÒ ¼ö ÀÖ´Ù. ÀÌ °úÁ¤À» °è¼Ó µÇÇ®ÀÌÇÏ¿©º¸´Ù ±ÙÁ¢ÇÑ ±Ù»ç°ªÀ» ¾òÀ» ¼ö ÀÖ´Ù." ¿ø±Ù¹ý¿¡ °üÇÑ Å×ÀÏ·¯ÀÇ ÀϺΠ³í¹®Àº ¿À´³¯ ºñÇà±â¿¡¼­ ÂïÀº »çÁøÀ¸·Î ø·®ÇÏ´Â »çÁø ø·®¹ýÀÇ ¼öÇÐÀû ³¸®¿¡ ÀÀ¿ëµÇ°í ÀÖ´Ù. Å×ÀÏ·¯´Â ÄÉÀӺ긮Áö ´ëÇÐÀÇ ¼º Á¸½º Ä®¸®Áö¿¡¼­ °øºÎÇÏ¿´À¸¸ç ÀÏÂïºÎÅÍ ¼öÇп¡ ¶Ù¾î³­ ¼ÒÁúÀ» º¸¿´´Ù. ±×´Â ¿µ±¹ Çмú¿ø ȸ¿øÀ¸·Î Çã¶ô ¹Þ¾ÒÀ¸¸ç, ±× °÷ÀÇ °£»ç°¡ µÇ¾úÀ¸³ª Àú¼ú¿¡ Àü³äÇϱâ À§Çؼ­ ¼­¸¥³× »ìÀÇ ³ªÀÌ¿¡ »çÀÓÇÏ¿´´Ù. ¸ÅŬ·Î¸° Àü°³¶ó ºÒ¸®´Â °ÍÀº ´ÜÁö ÄÉÀÏ·¯ Àü°³¿¡¼­ a=0ÀÎ °æ¿ìÀ̸ç, ¸ÅŬ·Î¸°ÀÌ (2vols., 1742)¿¡¼­ ±× °ÍÀ» »ç¿ëÇϱ⠼ö ³â Àü Å×ÀÏ·¯¿¡ ÀÇÇÏ¿© ¶ÇÇÑ ½ºÅиµ(James Stirling, 1692-1770)¿¡ ÀÇÇÏ¿© ½ÇÁ¦ÀûÀ¸·Î ¸í¹éÈ÷ ÁÖ¾îÁ³´Ù.

64. Colin Maclaurin (1698-1746), Professor Of Mathematics National Portrait Gallery, list of portraits for colin maclaurin including colinmaclaurin by Samuel Freeman, after Percey, colin maclaurin by Samuel http://www.npg.org.uk/live/search/person.asp?LinkID=mp51077

65. NPG D5179; Colin Maclaurin NPG D5179; colin maclaurin. colin maclaurin by Samuel Freeman, after Percey colin maclaurin (16981746), Professor of mathematics. http://www.npg.org.uk/live/search/portrait.asp?LinkID=mp55309&rNo=1&role=art

66. Colin Maclaurin- Famous Scots From Virtual Scotland colin maclaurin Famous Scots From Virtual Scotland. http://www.virtualscotland.co.uk/scotland_articles/famous-scots/colin-maclaurin.

window.status='Virtual Scotland ' Virtual Scotland Sections: Other Sections/Areas : (Isle of) (Isle of) (Harris) Virtual Scotland Free Stuff: (free) (Incl. Scottish) Colin Maclaurin- Famous Scots From Virtual Scotland Colin Maclaurin - A Famous Scottish Mathematician Colin Maclaurin Back to : - Famous Scots Virtual Scotland Shop: More Favourite Links: Support This Site : Web design Simply Top Limited Hosting by Simply Top Limited

67. Math Lessons - Colin Maclaurin Math Lessons colin maclaurin. colin maclaurin. colin maclaurin (February,1698 - June 14, 1746) was a Scottish mathematician. He was born in Kilmodan, http://www.mathdaily.com/lessons/Colin_Maclaurin

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... British mathematicians Colin Maclaurin Colin Maclaurin (February, June 14 ) was a Scottish mathematician He was born in Kilmodan, Argyll , and attended the University of Glasgow at age eleven (not unusual) and graduated at age fourteen. After graduation he remained at Glasgow to study divinity for a period and in , aged nineteen, he became professor of mathematics at Marischal College in the University of Aberdeen In he was appointed deputy of the mathematical professor at Edinburgh , James Gregory (brother of David Gregory and nephew of the more famous James Gregory ), upon the recommendation of Isaac Newton , who actually offered to pay Maclaurin's salary, so impressed was he with his work. Eventually, Maclaurin went on to succeed Gregory. The " Maclaurin series " for many trigonometric functions had in fact been developed and published by James Gregory before Maclaurin was even born, but Maclaurin wasn't aware of this and published them in Methodus incrementorum directa et inversa In he married Anne Stewart, the daughter of the

68. Porträt-Galerie + PORTRAIT-ANTIQUARIAT KLAUS HILLE / BERLIN + Translate this page maclaurin, colin. geb. 1698 gest. 1746 in Edinburgh. Schott. Mathematiker (sog.maclaurinsche Reihe). Brustbild in Oval, darunter Bildchen in Rechteck, http://www.portrait-hille.de/kap07/bild.asp?catnr1=2418&seqnr=1845

69. Miniaturbilder Zur Porträt-Galerie + PORTRAIT-ANTIQUARIAT KLAUS HILLE / BERLIN Translate this page xx, maclaurin, colin. xx, Brustbild in Oval, darunter Bildchen in Rechteck, dieBerechnung des Erdumfanges symbolisierend weibl. Figur mit 2 Globen, http://www.portrait-hille.de/kap07/Bildliste.asp?catnr1=2418

70. Colin Maclaurin Biography colin maclaurin biography and related resources. colin maclaurin (February,1698 June 14, 1746) was a Scottish mathematician. He was born in Kilmodan, http://www.biographybase.com/biography/Maclaurin_Colin.html

Biography Base Home Link To Us Search Biographies: Browse Biographies A B C D ... Z Colin Maclaurin Biography Colin Maclaurin (February, 1698 - June 14, 1746) was a Scottish mathematician. He was born in Kilmodan, Argyllshire, and attended the University of Glasgow at age eleven (not unusual) and graduated at age fourteen. After graduation he remained at Glasgow to study divinity for a period and in 1717, aged nineteen, he became professor of mathematics at Marischal College in the University of Aberdeen. In 1725 he was appointed deputy of the mathematical professor at Edinburgh, James Gregory (nephew of the more famous James Gregory), upon the recommendation of Isaac Newton, who actually offered to pay Maclaurin's salary, so impressed was he with his work. Eventually, Maclaurin went on to succeed Gregory. The "Maclaurin series" for many trigonometric functions had in fact been developed and published by James Gregory before Maclaurin was even born, but Maclaurin wasn't aware of this and published them in Methodus incrementorum directa et inversa.) In 1733 he married Anne Stewart, the daughter of the Solicitor General of Scotland. He actively opposed the Jacobite Rebellion of 1745 and assisted in the defence of Edinburgh but had to flee to York upon the approach of the Highlanders. He returned after the Jacobite army marched south, but the events had damaged his health, and led indirectly to his death.

71. Imago Mundi - Colin Mac-Laurin. m. en 1746 obtint dès 1717 la chaire de mathématiques au collège http://www.cosmovisions.com/MacLaurin.htm

Les gens Mac-Laurin Gregory Newton Daniel Bernouilli et Euler Geometria organica, Londres, 1720; , trad. par Lecozic, 1753; , 1748, trad. par Lavirotte, 1749. A B C D ... Z

72. Great Mathematicians maclaurin, colin, (16981746), Scotland, maclaurin Series. Cramer, Gabriel,(1704-1752), Swiss, The famous Cramer s Rule. Euler, Leonhard, (1707-1783) http://www.sali.freeservers.com/engineering/maths.html

Free Web Hosting Provider Web Hosting E-commerce High Speed Internet ... Photo Sharing if(window.ivnRotate) window.ivnRotate1 = new window.ivnRotate('ivnRotate1',0,document.awsSearch1.Keywords) Popular Searches: Home Page About Me Contact Me Photo Gallery 1 Photo Gallery 2 Family Album Engineering Stuff Sports Stuff Tennis Page Favorite People Links Galore Cool Links Kerala Page About Calicut HTML Tutorial Guest Book Home Page Engg. Home CFD Engg. Books ... NITT Faculty The finest mathematicians of all time who had a profound influence in the development of pure and applied mathematics Name Period Country Field of Contribution Descartes, Rene France Invented Analytical Geometry Fermat, Pierre de France Gregory, James Scotland Numerical Interpolation Newton, Isaac England Inventor of Differential and Integral Calculus Leibnitz, Gottfried Wilhem Germany Along with Newton he is also credited for invention of Calculus Raphson, Joseph England Numerical Integration Rolle, Michel France Rolle's Theorem Bernoulli, Jakob Swiss Mathematical Probability and Elasticity L'Hôpital, Guillaume François

73. Untitled Document “New Light on colin maclaurin,” Mathematical Association of America “Mathematics and the Modern State The Case of colin maclaurin,” American http://bernard.pitzer.edu/~jgrabine/CV_2004.html

74. American Mathematical Monthly, The: Newton, Maclaurin, And The Authority Of Math In Great Britain, Newton s most successful follower was colin maclaurin (16981746).maclaurin was the most significant Scottish mathematician and physicist http://www.findarticles.com/p/articles/mi_qa3742/is_200412/ai_n9520597

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Advanced Search Home Help IN free articles only all articles this publication Automotive Sports 10,000,000 articles - not found on any other search engine. FindArticles American Mathematical Monthly, The Dec 2004 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports Newton, Maclaurin, and the Authority of Mathematics American Mathematical Monthly, The Dec 2004 by Grabiner, Judith V Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. 1. INTRODUCTION: MACLAURIN, THE SCOTTISH ENLIGHTENMENT, AND THE "NEWTONIAN STYLE." Sir Isaac Newton revolutionized physics and astronomy in his book Mathematical Principles of Natural Philosophy [27]. This book of 1687, better known by its abbreviated Latin title as the Principia, contains Newton's three laws of motion, the law of universal gravitation, and the basis of all of classical mechanics. As one approaches this great work, a key question is: How did Newton do all of this? An equally important question is: Can Newton's methods work on any area of inquiry? Newton's contemporaries hoped that the answer to the second question was yes: that his methods would be universally effective, whether the area was science, society, or religion. What are the limits of the Newtonian method? In 1687, nobody knew. But his followers wanted to find out, and they tried to find out by applying these methods to every conceivable area of thought.

75. Otago Philosophy - 100 Level Papers James maclaurin, colin Cheyne. An investigation into fundamental issues concerningourselves and the world we live in. Does God exist? http://www.otago.ac.nz/philosophy/courses/100.html

new ypSlideOutMenu("menu1", "down", 28, 233, 281, 252) About Philosophy Department History Contact Events Seminar Social Conferences Courses Honours Postgraduate People Staff Tutors Office Hours Research Projects Links Jump to Course Materials 100 Level Papers The following is a list of the 100 level, first year papers available in the Philosophy Department in 2005. Click here for more information on papers offered and course requirements. PHIL 101 - Mind and Reality First Semester, Monday and Thursday, 12.00 noon. James Maclaurin, Colin Cheyne An investigation into fundamental issues concerning ourselves and the world we live in. Does God exist? What is the nature of our minds? Do we have freewill? What is the meaning of life? Second Semester, Tuesday and Friday, 12.00 noon. Alan Musgrave Scepticism is the view that nothing can be known for certain. This paper asks whether there is an adequate answer to scepticism. Questions tackled on the way include: Can we prove that ordinary physical things exist? Do we know what will happen tomorrow? Is there something especially certain about mathematical knowledge? What is truth? PHIL 103 - Ethical Issues Second Semester, Monday and Thursday, 12.00 noon.

76. Xah: Special Plane Curves: Trisectrix Of Maclaurin Trisectrix of maclaurin. Mathematica Notebook for This Page. History. This is acurve colin maclaurin (16981746) used to trisect an angle. http://www.xahlee.org/SpecialPlaneCurves_dir/TriOfMaclaurin_dir/triOfMaclaurin.h

If you spend more than 30 minutes on this site, please send $1 to me. Go to http://paypal.com/ and make a payment to xah@xahlee.org. Or send to: P. O. Box 390595, Mountain View, CA 94042-0290, USA. ☠Back to Table of Contents Trisectrix of Maclaurin Trisectrix of Maclaurin Mathematica Notebook for This Page History This is a curve Colin Maclaurin (1698-1746) used to trisect an angle. Description Formulas The following formula has asymtote at x=1 and loop point at origin: triOfMaclaurin.gcf Cartesian: y^2 (1-x) == x^2 (x + 3) triOfMaclaurin_polar.gcf Properties Relation to Parabola It is the pedal of parabola with repect to its focus reflect by the directrix. Trisecting an Angle Moving Point P Related Web Sites see Generic Reference Page MacTutor Famous Curve Index ☠Back to Table of Contents Content updated: 1998. Last modified: 2000/09/28. © 1995-97 by Xah Lee xah@xahlee.org ) http://xahlee.org/SpecialPlaneCurves_dir/specialPlaneCurves.html

77. E25 -- Methodus Generalis Summandi Progressiones The continental influence of maclaurin s treatise of fluxions. Leonhard andmaclaurin, colin of the Eulermaclaurin summation formula. http://math.dartmouth.edu/~euler/pages/E025.html

E25 Methodus generalis summandi progressiones (A general method for summing series) Summary: This paper leads to Bernoulli numbers from an integral of an infinite series and is called a beautiful triumph by Euler. According to the records, it was presented to the St. Petersburg Academy on June 20, 1732. Publication: Originally published in Commentarii academiae scientiarum Petropolitanae 6, 1738, pp. 68-97 Opera Omnia : Series 1, Volume 14, pp. 42 - 72 Reprinted in Comment. acad. sc. Petrop . 6, ed. nova, Bononiae 1743, pp. 61-94 [E25a] Documents Available: Original publication: (in the Commentarii The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E25 include: Calinger R., “Leonhard Euler: The first St Petersburg years (1727-1741).” Historia Mathematica, 23 (2), pp. 121-166 (May 1996). Dutka J., “On the summation of some divergent series of Euler and the zeta functions.” Archive for History of Exact Sciences, 50 (2), pp. 187-200 (1996). Ferraro G, Panza, M., “Developing into series and returning from series: A note on the foundations of eighteenth-century analysis.” Historia Mathematica, 30 (1), pp. 17-46 (Feb 2003).

78. Biografia De Maclaurin, Colin Translate this page maclaurin, colin. (Kilmodan, 1698-Edimburgo, 1746) Matemático británico. Ingresó enla universidad a la edad de 11 años, fue profesor en la de Aberdeen a http://www.biografiasyvidas.com/biografia/m/maclaurin.htm

Inicio Buscador Las figuras clave de la historia Reportajes Los protagonistas de la actualidad Maclaurin, Colin (Kilmodan, 1698-Edimburgo, 1746) Matemático británico. Ingresó en la universidad a la edad de 11 años, fue profesor en la de Aberdeen a los 19 y posteriormente en la de Edimburgo. Expuso un original método de generación de las cónicas en su obra Geometría orgánica (1720) y sentó las bases para una fundamentación lógica del cálculo infinitesimal en el Tratado de las fluxiones (1742). En su Tratado de álgebra (1748) aplicó el método de los determinantes a la resolución de ecuaciones con cuatro incógnitas. Inicio Buscador Recomendar sitio

79. Entrez PubMed colin Campbell maclaurin. No authors listed Publication Types Biography HistoricalArticle MeSH Terms History of Medicine, 20th Cent. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=3

80. MACL Definition Of MACL In Computing Dictionary - By The Free Online Dictionary, maclaurin series maclaurin, colin maclaurin, colin MacLaverty, Bernard Maclaw Maclay, William Maclay, William macle Maclean s http://computing-dictionary.thefreedictionary.com/MACL

Domain='thefreedictionary.com' word='MACL' Your help is needed: American Red Cross The Salvation Army join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia MACL 0.03 sec. Page tools Printer friendly Cite / link Email Feedback MACL Macintosh Allegro CL. E-mail: Mentioned in No references found Computing browser Full browser Macintosh Operating System Macintosh Toolbox Macintosh User Group Macintosh user interface ... MacIRMA MACL MacLink Plus MacLisp MacMinix MacNeal-Schwendler ... Macky Sall MACL MacLab MacLaine, Shirley MacLaine, Shirley MacLaines of Lochbuie ... Maclean, Donald Duart Word (phrase): Word Starts with Ends with Definition Free Tools: For surfers: Browser extension Word of the Day NEW! Help For webmasters: Free content NEW! Linking Lookup box ... Farlex, Inc. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.

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