1. Raphson Biography of Joseph Raphson (16481715) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Joeseph Raphson - A Brief History Joseph Raphson (16481715) Joseph Raphson was born in Middlesex in 1648, very little is known about his life, not even an obituary has been found. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Pantheist Association For Nature - Joseph Raphson Joseph Raphson. 16481715. By Gary Suttle. Cambridge intellectual Joseph Raphsonholds a special place among the lodestars of Pantheismrecent scholarship http://home.utm.net/pan/raph-son.html

Joseph Raphson By Gary Suttle References . Edited by Philip McGuinness, Alan Harrison, and Richard Kearney. Dublin, Ireland: The Lilliput Press, 1997. . Personal Communication, October, 28, 2002 and November 18, 2002. Dr. Daniel relates "When I ran across Raphson's Latin use of pantheos and pantheismus in 1994, I think I was simply following up on a reference to Raphson by Berkeley (in his "Philosophical Commentaries"). Most Berkeley scholars are not as familiar with Toland as I probably am, so the appearance of the terms struck me (since I, like everyone else, had thought that Toland was the first to use them). Probably people knew of Raphson's use of the terms but had not made the connection about who used them first. At least in 1994 I was still under the impression that Toland had used the term first. When I mentioned it to (a fellow scholar), he suggested that I contact the folks at the Oxford English Dictionary to update their entry. But since the OED deals with English uses, I did not because Toland still would have been the first to use the English versions. However, as Toland notes in "Serena," Raphson seems to have come up with the concepts of pantheism and pantheist in 1697. I guess I may have been the first to have seen that, primarily in the Toland-Berkeley context (of which latter relation there is a lot more to sayand I am currently working on it for a book on Berkeley)." Hanson, Ken.

4. Re Joseph Raphson By Jeff Miller Re Joseph Raphson by Jeff Miller. Back to messages on this topic Back to mathhistory-list previous next http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Re Joseph Raphson By David Fowler Re Joseph Raphson by David Fowler. Back to messages on this topic Back to mathhistory-list previous http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. University Of South Carolina System University of South Carolina System http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Joseph Raphson HOLISTIC NUMERICAL METHODS INSTITUTE Committed to bringing numerical methods to undergraduates Joseph Raphson 16481715 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. References For Raphson References for the biography of Joseph Raphson http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Newton, Halley, Cunn And Raphson (1720) Universal Arithmetick, Or Author Cunn Author Raphson, Joseph PUBLISHER Printed for J. Senex , W. Taylor , T. Warner and J. Osborn (London) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Newton's Method of . The method is attributed to Sir Isaac Newton (16431727) and Joseph Raphson (1648-1715). Theorem (Newton-Raphson Theorem). http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Mathematics Pronunciation Guide Bernoulli's law G. G. Berry Berry's paradox Joseph L. F. Bertrand Fredrich Wilhelm Bessel 17841846 'bess uhl beta 'bay duh http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Raphson Biography of joseph raphson (16481715) joseph raphson s life can only bededuced from a number of pointers. No obituary of raphson seems to have been http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Raphson.html

Joseph Raphson Born: 1648 in Middlesex, England Died: Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Joseph Raphson 's life can only be deduced from a number of pointers. No obituary of Raphson seems to have been written and we can now only piece together details about his life from records which exist such at University of Cambridge records and records of the Royal Society . It is through the University of Cambridge records that we know that Raphson attended Jesus College Cambridge and graduated with an M.A. in 1692. Rather remarkably Raphson was made a member of the Royal Society in 1691, the year before he graduated. His election to that Society was on the strength of his book Analysis aequationum universalis which was published in 1690 contained the Newton method for approximating the roots of an equation. In Method of Fluxions Newton describes the same method and, as an example, finds the root of x x - 5 = lying between 2 and 3. Although written in 1671 it was not published until 1736, so Raphson published the result nearly 50 years before Newton Raphson's relation to Newton is important but not particularly well understood. In [2] Copenhaver writes:-

13. References For Raphson References for the biography of joseph raphson. DJ Thomas, joseph raphson,FRS, Notes and Records Roy. Soc. London 44 (2) (1990), 151167. http://www-groups.dcs.st-and.ac.uk/~history/References/Raphson.html

References for Joseph Raphson Version for printing Articles: N Bi'cani'c and K H Johnson, Who was 'Raphson'?, Internat. J. Numer. Methods Engrg. B Copenhaver, Jewish Theologies of Space in the Scientific Revolution: Henry More, Joseph Raphson, Isaac Newton and their Predecessors, Annals of Science D J Thomas, Joseph Raphson, F.R.S., Notes and Records Roy. Soc. London Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Raphson.html

14. Pantheist Association For Nature - John Toland (joseph raphson, a Cambridge mathematician, originated the words pantheist and pantheism in a 1697 theological work written in Latin. http://home.utm.net/pan/toland.html

John Toland By Gary Suttle Lexicographers credit John Toland with the first English language usage of the word "pantheist." Toland set forth precepts of Pantheism and even described membership activities for a Pantheist Society. Biographers describe Toland as a swashbuckling adventurer in scholarshipa philosopher, a writer, a linguist, a polemicist, a diplomat, a biblical scholar, a freethinker, a deist, and ultimately a proponent of Pantheism. His fascinating life began near Londonderry, Ireland, on November 30, 1670. Christened in the Catholic Church, he converted to Protestantism around age 15. Education led him from Christianity to freethinking. Toland acquired a degree from the University of Edinburgh in 1690. He studied further in England, Germany, and Holland. A Dutch friend called Toland as "a free-spirited, ingenious man." But his unorthodox views and outspokenness made it hard to earn a living. He gained income by penning political pamphlets and biographies for aristocratic patrons. Toland wrote prolifically on a wide range of subjects, including religious tolerance and civil liberty. A large bibliography lists almost two hundred works authored or ascribed to him. An important early book

15. Joseph Raphson The life of joseph raphson (16481715) is one that is shrouded in mystery andrather difficult to follow. In fact no obituary of raphson appears to have http://numericalmethods.eng.usf.edu/anecdotes/raphson.html

Milwaukee School of Engg HOLISTIC NUMERICAL METHODS INSTITUTE Committed to bringing numerical methods to undergraduates Joseph Raphson De spatio reali was a work which dealt with Raphson's vision of space, called 'real space'. He thought of space as being independent of the mind that perceives it. In this work he also discussed the infinite (potential and actual) and motion in space, where space is said to be infinite, but the objects in it are finite. Demonstratio de deo dealt with the issue of space and Raphson's Cabalist ideals. As an ironic twist, Newton views of space were strongly influenced by religion, the Christian religion and philosophy. All Rights Reserved Questions, suggestions or comments, contact kaw@eng.usf.edu

16. Newton's Method: Information From Answers.com In 1690, joseph raphson published a simplified description in Analysis aequationumuniversalis. raphson again viewed Newton s method purely as an algebraic http://www.answers.com/topic/newton-s-method

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Newton's method Wikipedia Newton's method In numerical analysis Newton's method (or the Newton-Raphson method ) is an efficient algorithm for finding approximations to the zeros (or roots) of a real -valued function . As such, it is an example of a root-finding algorithm . It can also be used to find a minimum or maximum of such a function, by finding a zero in the function's first derivative, see Newton's method as an optimization algorithm Description of the method The idea of the method is as follows: one starts with a value which is reasonably close to the true zero, then replaces the function by its tangent (which can be computed using the tools of calculus ) and computes the zero of this tangent (which is easily done with elementary algebra). This zero of the tangent will typically be a better approximation to the function's zero, and the method can be iterated Suppose f a b R is a differentiable function defined on the interval a b ] with values in the real numbers R . We start with an arbitrary value x (the closer to the zero the better) and then define for each natural number n Here

17. Great Mathematicians raphson, joseph, (16481715), England, Numerical Integration. Rolle, Michel,(1652-1719), France, Rolle s Theorem. Bernoulli, Jakob, (1654-1705), Swiss 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

18. Newton's Method The Newtonraphson (or simply Newton s) method is one of the most useful and bestknown to Sir Isaac Newton (1643-1727) and joseph raphson (1648-1715). http://math.fullerton.edu/mathews/n2003/Newton'sMethodMod.html

Module for Newton's Method If are continuous near a root , then this extra information regarding the nature of can be used to develop algorithms that will produce sequences that converge faster to than either the bisection or false position method. The Newton-Raphson (or simply Newton's) method is one of the most useful and best known algorithms that relies on the continuity of . The method is attributed to Sir Isaac Newton (1643-1727) and Joseph Raphson Theorem ( Newton-Raphson Theorem Assume that and there exists a number , where . If , then there exists a such that the sequence defined by the iteration for will converge to for any initial approximation Proof Newton-Raphson Method Newton-Raphson Method Algorithm ( Newton-Raphson Iteration To find a root of given an initial approximation using the iteration for Computer Programs Newton-Raphson Method Newton-Raphson Method Mathematica Subroutine (Newton-Raphson Iteration). Example 1. Use Newton's method to find the three roots of the cubic polynomial Determine the Newton-Raphson iteration formula that is used. Show details of the computations for the starting value

19. Newton-Raphson Method The Newtonraphson method allows one to solve equations of the form f(x) = 0 by Later, in 1690, joseph raphson found an improvement to Newton s method http://home.att.net/~srschmitt/newtons_method.html

home send comment send link add bookmark Solving equations with the Newton-Raphson method by Stephen R. Schmitt Introduction The Newton-Raphson method allows one to solve equations of the form f(x) = by finding the values of x for which the equality is valid. In 1669, Isaac Newton found an algorithm to solve for the roots (values for which the function equals zero) of a polynomial equation. In this method, one guesses a starting value and then repeatedly makes small changes that yield improved approximations to the solution. The process terminates once the desired precision is reached. Newton's original method did not use the derivative of f(x) Later, in 1690, Joseph Raphson found an improvement to Newton's method which did use the derivative of f(x), f'(x) . Each iterative step of the Newton-Raphson method is x n+1 := x n - f(x n )/f'(x n If an estimated root of f(x) = is x n , then the line tangent to f(x n at x n crosses the x-axis at a point, x n+1 , which is an improved estimate of the root. The slope of this tangent is given by the derivative. Repeated application of the iterative step improves the estimate. Approximate derivative Sometimes it is inconvenient to explicitly determine the derivative of a function for use in a computer program. An approximate derivative of

20. British Journal For History Of Science, 1992, 25, 347-54 A recent appreciation of joseph raphson discussed the historically perceiveddifference 34 DJ Thomas, ‘joseph raphson, FRS’, Notes Rec. Roy. Soc. http://www.ucl.ac.uk/sts/nk/newtonapprox.htm

AN ENDURING MYTH N. KOLLERSTROM British Journal for History of Science,1992, 25, 347-54 (I) -2y-5 = 0, as the example given in De analysi, he started with the approximate solution of 2. Let the exact solution be 2+p, where p is small, and substitute 2+p into the equation in place of y. This generates a new cubic equation, namely p +10p = 1. As p is small, its powers are ignored, yielding the approximate solution 10p = 1 or p = 0.1. Next, 0.1+q is inserted in place of p to form another new equation, and so on. This is continued to achieve any desired level of accuracy. Raphson presented his method as follows. Taking as an example the equation ba - aaa = c (which we would write as a - ba + c = 0), let an approximate solution be g. Then, if a more accurate solution is g+x, X = (c+ggg-bg) / (b-3gg) The quotient expression was obtained by a two-step procedure (13). In the above example, one substituted (g + x) for a, then expanded the power terms to give a larger equation; this was a straightforward binomial expansion. The second step was to extract the terms in x: the terms which multiplied x in this example were (b-3gg), and these became the quotient. Iterating this procedure, Raphson explained, would give any desired level of accuracy. He elaborated his method only within the context of polynomial equations, without attempting to deal with reciprocal or square root functions. His worked examples contained terms up to the seventh power.

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