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         Gerson Levi Ben:     more detail
  1. The Astronomy of Levi ben Gerson (1288-1344): A Critical Edition of Chapters 1-20 with Translation and Commentary (Studies in the History of Mathematics and Physical Sciences) by Bernard R. Goldstein, 1985-07-15
  2. The Astronomical Tables of Levi Ben Gerson (Connecticut Academy of Arts & Sciences Series, Vol 45) by Bernard R. Goldstein, 1974-06
  3. Philosophie religieuse de Lévi-Ben-Gerson (French Edition) by Isidore. Weil, 1868-01-01
  4. Astronomy of Levi Ben Gerson, 1288-1344
  5. Levi Ben Gerson's Prognostication for the Conjunction of 1345 (Transactions of the American Philosophical Society) by Bernard R. Goldstein, David Pingree, 1990-11
  6. Preliminary remarks on Levi ben Gerson's contributions to astronomy, (Israel Academy of Sciences and Humanities. Proceedings) by Bernard R Goldstein, 1969
  7. R. Levi Ben Gerson: A bibliographical essay by Menachem Marc Kellner, 1979
  8. Introduction to the History of Science. Volume 3, Science and Learning in the Fourteenth Century. Part I, The Time of Abu-l-Fida, Levi ben Gerson, and William of Occam (First half of the fourteenth century) by G. Sarton, 1962
  9. Sefer Maassei Choscheb. Die Praxis des Rechners. Ein hebraisch-arithmetisches Werk des Levi Ben Gerschom aus dem jahre 1321. by Gerson (ed.). Levi ben Gershom [GERSONIDES]; LANGE, 1909-01-01

21. Yale University Library
Naples. Zi +6737. Perush ha Torah. levi ben gerson. 14746. Mantua. Zi +6906. Perushha Torah. Zi +6741. Perush Iyob . levi ben gerson. 1477. Ferrara. Zi 5745.
http://www.library.yale.edu/judaica/incunab.html
The Collection / 15th-century Incunabula / 16th-century Hebrew imprints Bibliographies Hebrew Periodicals Micorform Notable New Acquisitions / Texts on CD ROM Yiddish Periodicals Yizkor Books The Judaic Studies Reading Room ... Contact Us 15th-Century Incunabula Below is a list of incunabula in alphabetical order by title. The citation includes title, author, place of publication, year published, and Yale University Library call number. All these incunabula are housed in the Beinecke Rare Book and Manuscript Library. If you have any questions locating the materials, please speak to Nanette Stahl , the Curator of the Judaica Collection To Search This Web Page by Title, Author, or Place of Publication:
  • From "Edit" on the Menu Bar, go to "Find" Type in your search word and hit enter.
  • 22. Tekiah - My Beliefs About God
    levi ben gerson, according to author Jeffrey Schein, had very clear ideasabout God and why bad things are allowed to happen to good people.
    http://www.tekiah.com/bio/beliefs.html

    Home
    Classes Schedule Exercises ... Search Site The most beautiful thing we can experience is the mysterious.
    - Albert Einstein
    My Beliefs About God
    Contemplating one's belief in God can literally open up a can of worms. Committing to the existence or non-existence of a higher power forces you to take a stand about many other facets of being alive. In fact, contemplating God creates a snowball effect with regard to one's beliefs about our entire reason for being. I've come to feel God as an energy system that is located on a different plane of existence. We are all a part of that existence, but in that other realm, we are unable to experience anything but pure love. On the earth plane, God challenges us to choose love despite our exposure to numerous other feelings and experiences. God's interference with our everyday activities would only hinder this plan. In fact, if we all began to act more "Godly" here on earth, we may someday bring a more heavenly existence to the denser plane. Encountering a Jewish philosopher with views akin to mine has renewed my interest in Jewish knowledge and ideas. The fact that Ben Gerson invented the instrument that allows astronomers and astrologers (like me) to be able to measure the angular relationship between celestial bodies is just one in a strange line of synchronicities that has led my meandering spiritual quest back to Judaism. Home Classes Schedule Exercises ... About Dina April For more info, contact

    23. Doron Zeilberger's 36th Opinion:
    Written March 5, 1999. Rabbi levi ben gerson, in his prealgebra text (1321), SeferMa'asei Khosev, had about fifty theorems, complete with rigorous proofs.
    http://www.math.temple.edu/~zeilberg/Opinion36.html
    Opinion 36: Don't Ask: What Can The Computer do for ME?, But Rather: What CAN I do for the COMPUTER?
    By Doron Zeilberger
    Written: March 5, 1999 Rabbi Levi Ben Gerson, in his pre-algebra text (1321), Sefer Ma'asei Khosev, had about fifty theorems, complete with rigorous proofs. Nowadays, we no longer call them theorems, but rather (routine) algebraic identities. For example, proving (a+b)*c=a*c+b*c took him about half a page, while proving (a-b)*c+a*(b-c)=b*(a-c) took a page and a half, and proving a*(b*c*d)=d*(a*b*c) took him one page. The reason that it took him so long is that while he already had the algebraic concepts, he still was too hung-up on words, and while he used symbols, (denoted by dotted Hebrew letters), he did not quite utilize, systematically, the calculus of algebraic identities. The reason was that he was still in a pre-algebra frame of mind, and it was more than three hundred years later (even after Cardano), that probably Viete started the modern `high-school' algebra. So Levi Ben Gerson had an inkling of the algebraic revolution to come, but still did not go all the way, because we humans are creatures of habit, and he liked proving these deep theorems so much that it did not occur to him to streamline them, and hence kept repeating the same old arguments again and again in long-winded natural language.

    24. Contents Of Current Volumes
    ARTICLES. 15. BR Goldstein levi ben gerson's Preliminary Remarks for a Theory ofPlanetary Latitudes. 31. JL Mancha levi ben gerson's Star List for 1336. 59.
    http://www.alephj.huji.ac.il/Contents.htm
    The Hebrew University of Jerusalem
    Aleph Abstracts ARTICLES B.R. Goldstein
    Levi ben Gerson's Preliminary Remarks for a Theory of Planetary Latitudes J.L. Mancha
    Levi ben Gerson's Star List for 1336 Francisco Moreno-Carvalho
    A Newly-Discovered Letter by Galileo Galilei . Contacts Between Galileo and Jacob Rosales (Manoel Bocarro Francês), a Seventeenth-Century Jewish Scientist and Sebastianist Hans Lausch
    "The Ignorant Hold Back Their Judgement and Await the Conclusions of the Knowing" — Moses Mendelssohn and Other Mathematicians David B Ruderman
    Some Jewish Responses to Smallpox Prevention in the Late Eighteenth and Early Nineteenth Centuries: A New Perspective on the Modernization of European Jewry David A. Hollinger
    Why Are Jews Preeminent in Science and Scholarship? The Veblen Thesis Reconsidered
    DISCUSSION FORUM
    On Yehuda Liebes’ recent Torat Ha-yesirah sel Sefer Yesirah Y. Tzvi Langermann
    On the Beginnings of Hebrew Scientific Literature and on Studying History Through “ Maqbilot ” (Parallels) David Shulman
    Sefer Yesirah
    and Sanskrit Linguistics Steve Wasserstrom
    Further Thoughts on the Origins of Sefer Yesirah
    Brief Communications
    Tony L vy A Newly-Discovered Partial Hebrew Version of Al-Khwarizmi’s Algebra Ruth Glasner Levi ben Gershom (Gersonides) Cyrill Aslanov Joseph Ibn Kaspi John North Essay Review Some Jewish Contributions to Iberian Astronomy.

    25. Welcome To RealOlam.com ! - Jewish Community ISP, Exclusive News And Content
    Little is known of his life except that he was on friendly t FULLSTORY . levi ben gerson Born 1288 in Bagnols, Gard, France
    http://www.realolam.com/channels/default.asp?channel=45&linkid=302

    26. Welcome To RealOlam.com ! - Jewish Community ISP, Exclusive News And Content
    levi ben gerson JJO'Connor and EF Robertson, Biographies. Born 1288in Bagnols, Gard, France Died 1344 levi ben gerson wrote Book
    http://www.realolam.com/channels/default.asp?channel=45&articleid=3743

    27. Abteilung Für Mittelalterliche Geschichte, Uni Tübingen: Linksammlung Judentum
    Pablo de Burgos oder Pablo de Cartagena, levi ben gerson, auch gersonides
    http://www.uni-tuebingen.de/mittelalter/links/alllinks5c.htm

    Startseite

    Aktuelles

    Abteilung

    Studium
    ...
    Uni Tübingen

    Juden im Mittelalter
    Das Judentum und die Gilden: Wirtschaft und Konkurrenz im Mittelalter
    Durften Frauen im Mittelalter zur Thora gerufen werden? Meir von Rothenburg- Der Maharam Leben und Werk des Mosche ben Maimon (Maimonides) ... Was hat Weinbau mit dem Berufsrabbinertum zu tun? Raschi von Troyes und die Thora als Spaten sowie weitere Artikel
    Beziehungen - Juden und Christen im Mittelalter

    Einführung zur Geschichte der Juden in Mittel- und Osteuropa
    mit jeweils Abschnitten zum Mittelalter, Vortragsreihe an der Münchner VHS, von haGalil
    Der Beitrag der Juden zum städtischen Haushalt des Mittelalters
    Arbeit aus einem Hauptseminar der HU-Berlin, mit Bibliographie Die Juden im Wirtschaftsleben: Jüdische Geldleihe im 14. Jahrhundert Arbeit aus einem Proseminar der Uni Trier, mit Bibliographie Judenverfolgung während des ersten Kreuzzuges (Beispiel Trier) Arbeit aus einem Proseminar zur Geschichte der Juden im Früh - und Hochmittelalter, Universität Regensburg, mit Bibliographie

    28. Der Jakobstab, Winklemessinstrument Der Alten Seefahrer
    Translate this page auch rückwärts (Bild 4). Die erste bekannte sachkundige Beschreibung stammt vomjüdischen Gelehrten levi ben gerson aus Bagnolos in Katalonien (1288-1344).
    http://home.t-online.de/home/miffland/jakobstb.htm
    Der Jakobstab, Winkelmessinstrument der alten Seefahrer
    In der Folgezeit entwickelten sich die Maueren/Sarazenen zu hervorragenden Astronomen. So haben noch heute viele Fixsterne arabische Namen (z.B. Benetnasch, Beteigeuze, Schedir).
    Astrolabium Quadrant
    Obwohl der Jakobstab bereits 1433 von Paolo Toscanelli (1397 - 1482) erfolgreich zur Ortsbestimmung eines Kometen verwendet worden war, konnte er sich in der Seefahrt, trotz der erheblichen Vereinfachung im Gebrauch durch Regiomontanus, erst ab dem 16. Jahrhundert durchsetzen.
    Der Nachbau eines Jakobstabes von Wilhelm Dorenbusch, ist beim Arbeitskreis Norderney der Wilhelm-Dorenbusch-Sternwarte auf Norderney zu besichtigen.

    29. Gersonides - Wikipedia
    Rabbi levi ben gerson (Gershon), better known as gersonides or the Ralbag (1288—1344),was a Jewish philosopher and commentator, was born at Bagnols in
    http://www.wikipedia.org/wiki/Gersonides
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    Gersonides
    From Wikipedia, the free encyclopedia. Rabbi Levi ben Gerson (Gershon), better known as Gersonides or the Ralbag (1288—1344), was a Jewish philosopher and commentator, was born at Bagnols in Languedoc, probably in 1288.
    Biography
    As in the case of the other medieval Jewish philosophers little is known of his life. His family had been distinguished for piety and exegetical skill, but though he was known in the Jewish community by commentaries on certain books of the Bible , he never seems to have accepted any rabbinical post. Possibly the freedom of his opinions may have put obstacles in the way of his preferment. He is known to have been at Avignon and Orange during his life, and is believed to have died in 1344, though Zacuto asserts that he died at Perpignan in 1370.
    Works
    Part of his writings consist of commentaries on the portions of Aristotle then known, or rather of commentaries on the commentaries of Averroes. Some of these are printed in the early Latin editions of Aristotle’s works. His most important treatise, that by which he has a place in the history of philosophy, is entitled "Milhamot Adonai", The Wars of God, and occupied twelve years in composition (1317—1329). A portion of it, containing an elaborate survey of astronomy as known to the Arabs, was translated into Latin in 1342 at the request of Clement VI.

    30. Induction In Islamic Mathematics And Medieval European
    mathematics. The topics covered consisted of Dahshour Egypt, AlKaraji,levi ben gerson (1288-1344), and proposition forty-one.
    http://public.csusm.edu/public/DJBarskyWebs/330CollageOct03.html
    Induction in Islamic Mathematics and Medieval European Mathematics
    This presentation given today by A.J. Lundgren, after Dr. Barsky's commentary on today in math history, began to generate an overall theme of induction in European mathematics. The topics covered consisted of Dahshour Egypt, Al-Karaji, Levi ben Gerson (1288-1344), and proposition forty-one. Today's discussion actually began with more on Islamic mathematics. In particular, al-Karaji and an inductive argument that deals with a certain arithmetic sequence. He proved the formula for the sum of the integral cubes. What is interesting about al-Karaji's proof, is that he doesn't state a general result for an arbitrary n. His theorem is stated with 10 and works backwards to 1. As we moved to medieval Europe, we learned about Levi ben Gerson. He invented the Jacob Staff which was used to measure the angular separation between heavenly bodies. He dealt with combinatorics in a major work of his, The Art of the Calculator. The most important parts of this are the theorems and their proofs. As we looked at proposition 41, which was the proof of the formula for the sum of the first n integral cubes, we saw that Levi first proves the inductive step, this allows you to move from k to k + 1.

    31. Important Message From Doron Zeilberger
    PA 19122, zeilberg@math.temple.edu, http//www.math.temple.edu/~zeilberg/ WrittenMarch 5, 1999 Revised March 25, 1999 Rabbi levi ben gerson, in his pre
    http://pauillac.inria.fr/algo/AofA/mailing_list/msg00113.html
    ANALYSIS of ALGORITHMS, Bulletin Board Date Prev Date Next Thread Prev Thread Next ... Thread Index
    Important message from Doron Zeilberger
    http://www.math.temple.edu/~zeilberg/ http://www.math.temple.edu/~zeilberg/ http://www.math.temple.edu/~zeilberg/programs.html )., in particular RENE ( http://www.math.temple.edu/~zeilberg/tokhniot/RENE http://www.wits.ac.za/helmut/index.htm

    32. Abraham Ibn Ezra
    It was Rabbi levi ben gerson, in 1321, who rigorously proved the explicit expressionsfor the binomial coefficients, and even he, almost two hundred years later
    http://www.geocities.com/Paris/Palais/1067/ibn_ezra02.html
    The Planets Are Servants
    What else can you tell me about this Ibn Ezra? Well, he also knew how to compute the seventh row of what later became to be called Pascal's triangle. The practical problem that inspired these calculations was to find the number of possible planetary conjunctions. As every educated person knows, there are exactly seven planets: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. Whenever a subset of cardinality larger than one shows up at the same sign, this has great astrological significance. How many such events are possible? Here is a translation, from Hebrew, of the first half of the relevant passage in Ibn Ezra's Sefer HaOlam. He called planets 'servants' ( meshartim ), which perhaps meant servants of God. And the combinations are hundred and twenty. And thus you can know their number. [It is] Known that every calculation that adds from one to any number that one wills, you can obtain by its value [multiplied] by its half together with half of one, and here is an example, we wanted to know what is the sum of the numbers from one to twenty. We will multiply twenty by its half and half of one, and [we get] two hundreds and ten. And now we can start to know how many combinations [involving] two servants. And it is known that the number of servants is seven. And Saturn can combine with six other servants. And six by its half and the half of one is one and twenty. And thus is the number of combinations of twos. [Now] we wanted to know the number of combinations of threes. Here we put Saturn and Jupiter and one of the others, their number is five. We multiply five by two and a half and a half, and get fifteen...

    33. Fiancé/Groom Fiancée/Bride Père Du Fiancé/Groom's Father's
    ben Zonana Oro Boulisa, benoliel Judah, ben Zonana Moses, levi Fubini Hezekiah, BachiColombina, levi Fubini Moses, Colomba, meha-Hazanim (Cantarini) gerson ha-Cohen,
    http://www.geocities.com/EnchantedForest/1321/ketub1.html
    Index de l'ouvrage de Shalom Sabar "Mazal Tov"
    Alphabetical index of Shalom Sabar's book "Mazal Tov"

    The Israel Museum, Jerusalem, 1993
    Index par noms des fiancés/Index by grooms names Fiancé/Groom Fiancée/Bride Père du fiancé/Groom's Father's name Père de la fiancée/Bride's Father's name Année/Year Ville/Town Page Abraham Bruria Elijah Joseph Isfahan (Iran) Abuzaglo Judah Adrehi Freha (or Freja) Abuzaglo Mas'oud Adrehi Joseph Faro (Portugal) Afriat Jacob Afriat Aysha Afriat Joseph Afriat Abraham Essaouira (Mogador) (Morocco) Agha Muhammed Sadic Sarref Nasttar Khanom Muhammed Ismail Karbalai Abdul Meshed (Iran) Al-Cohen al-'Araqi Abraham Al-Sheikh al-Levi Rummiyyeh Al-Cohen al-'Araqi Mussa Al-Sheikh al-Levi Abraham Salem San'a (Yemen) Amron Gabriel Mi-Segni (Di Segni) Simha Amron Hezekiah Mi-Segni (Di Segni) Shabbetai Rome (Italy) Aryeh Kalman Ben Zevi Jochebed Aryeh Judah Ben Zevi Israel Singapore Ashkenazi Isaac Alfandari Fiora Ashkenazi Eliezer Alfandari Jacob Ferrara (Italy) Babai Fatou (?) Mordecai Yekutiel Yezd (Iran) Baer Nehemiah Nissim mi-Ascoli (Da Ascoli) Rosa Baer Shabbetai Haïm mi-Ascoli (Da Ascoli) Isaac Pesaro (Italy) Barchilon Isaac Hasan Leah Barchilon Jacob Hasan David Tetouan (Morocco) Ben Attaouil Salomon Benzaquen Rachel Ben Attaouil Jacob Benzaquen Isaac Gibraltar Bendelac Menahem Abudarham Dona Bendelac Samuel Abudarham Menahem Gibraltar Benoliel Daniel Joseph Ben Zonana Oro Boulisa Benoliel Judah Ben Zonana Moses Roma (Italy) Bueno Jacob Hananiah Bueno Gracia Bueno Joseph Bueno David Venice (Italy) Cantarini see me-ha-Hazanim Cohen Jacob Haï

    34. 5:1 (Spring 1997)
    The Physical astronomy of levi ben gerson. levi ben gerson (12881344) was a medievalastronomer who responded in an unusual way to the Ptolemaic tradition.
    http://www.phil.vt.edu/pos/5-1.htm
    5:1 (Spring 1997) The Physical astronomy of Levi ben Gerson Bernard R. Goldstein Almagest , he discovered a new phenomenon of Mars and noticed a serious flaw in Ptolemy’s treatment of the Moon. Calibration Allan Franklin A Twentieth-Century Phlogiston: Constructing Error and Differentiating Domains Douglas Allchin

    35. Biography-center - Letter G
    Gershwin, George www.pbs.org/wnet/americanmasters/database/gershwin_g.html; gerson,levi ben wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/levi.html;
    http://www.biography-center.com/g.html
    Visit a
    random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish
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    523 biographies

    • www.pathfinder.com/time/time100/scientist/profile/godel.html
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    • G.i., American
      www.pathfinder.com/time/time100/heroes/profile/gi01.html
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      www.grandprix.com/gpe/drv-gabbep.html
    • Gabelich, Gary
      www.hickoksports.com/biograph/gabelichg.shtml
    • Gable, Daniel M. www.hickoksports.com/biograph/gabledan.shtml
    • Gabor, Dennis www.nobel.se/physics/laureates/1971/gabor-autobio.html
    • Gachot, Bertrand www.grandprix.com/gpe/drv-gacber.html
    • Gaddi, Taddeo www.kfki.hu/~arthp/bio/g/gaddi/taddeo/biograph.html
    • Gadgil, Ashok web.mit.edu/invent/www/inventorsA-H/gadgil.html
    • Gadgil, Ashok

    36. Biography-center - Letter L
    levi, Primo www.uwgb.edu/galta/333/bios98/levi.htm; levi ben gerson,wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/levi.html;
    http://www.biography-center.com/l.html
    Visit a
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    540 biographies

    37. Philosophie - Mitglieder
    Translate this page Veröffentlichungen Die Intellektlehre des levi ben gerson in ihrer Beziehung zurchristlichen Scholastik, Frankfurt / Main, New York, Paris 1991 (Europäische
    http://www.uni-oldenburg.de/philosophie/mitglieder/möbuß.html
    B iographie
    Geboren am 10.01.1963 in Hannover, Studium der Philosophie und Geschichte in Hannover.
    V eröffentlichungen
    Der Begriff der cientia bei Levi ben Gerson, in: Miscellanea Mediaevalia 22 (1994) 653-666.
    Weiblichkeitsvisionen der Mystikerinnen im Mittelalter, in: Die Krise der Kategorie, hrsg. vom 'Verein sozialwissenschaftliche Forschung und Bildung' , Frankfurt am Main 1994, S. 125-145.
    Die Erscheinung des Transzendenten, Eilah Delmedigo und der Averroismus der Renaissance, Hannover 1996.
    Schopenhauer für Anfänger, "Die Welt als Wille und Vorstellung". Eine Lese-Einführung, München 1998.
    Sartre, Freiburg 2000.
    A ktuelle Forschungsschwerpunkte
    jüdische Philosophie des Mittelalters und der Renaissance
    französische Gegenwartsphilosophie Seitenanfang

    38. Ivars Peterson's MathLand
    The basic formulas for finding permutations and combinations can befound in the writings of levi ben gerson (12881344). There's
    http://www.maa.org/mathland/mathland_1_20.html
    Ivars Peterson's MathLand January 20, 1997
    Fragments of the Past
    The early history of mathematics is like a jigsaw puzzle missing many of its pieces. Historians and mathematicians have been painstakingly filling in the blanks, gradually constructing a richer, more complete story of how and where mathematical thought originated and spread. One period of considerable interest is that between the decline of Greek mathematics, coinciding with the collapse of the western Roman Empire in the fifth century, and the rise of European mathematics in the fifteenth century. Mathematics professor Morris Kline of New York University's Courant Institute of Mathematical Sciences expressed a common view of that period in his 1972 book Mathematical Thought from Ancient to Modern Times . "The Arabs made no significant advance in mathematics," he wrote. "What they did was absorb Greek and Hindu mathematics, preserve it, and ultimately, ... transmit it to Europe." In other words, Islamic scholars did little more than put Greek mathematics into cold storage until Europe was ready to accept it. Historian George G. Joseph challenged that view in his provocative book

    39. Die Ausstellung Juden An Der Universität Heidelberg
    Translate this page Heidelberg 1909. Dissertation. levi ben gerson (1288-1344) war Talmudgelehrter,Mathematiker und Astronom. Nach Maimonides gilt
    http://wwwnp.tphys.uni-heidelberg.de/Ausstellung/show.cgi?de&B&12&074

    40. Math 300 Guidelines For Papers
    ibn Qurra Gerbert d'Aurillac Ibn alHaytham Mohammad al-Biruni Omar Khayyam Nasiral-Din al-Tusi Leonardo of Pisa Qin Jiushao levi ben gerson Nicole Oresme
    http://cerebro.cs.xu.edu/math/math300/02s/papers.html
    Math 300 Great Moments in Mathematics
    Spring 2002
    Guidelines for papers
    You will prepare two research papers for this course:
    • a biographical paper, due February 21 , that relates the mathematical career of a noted historical figure born before 1700; and a paper due April 18 that performs a critical reading of an original source of importance in the history of mathematics.
    Your biographical paper should conform to the following guidelines, listed in order of importance, and will be evaluated against them:
    • The paper should present a comprehensively researched discussion of the life history of your chosen mathematician; this person's significant mathematical accomplishments must be thoroughly discussed. (35%) It should be presented in a clear and coherent writing style , using correct spelling, proper pronunciation and good grammar. (25%) It should contain a bibliography with at least three sources including at least three print-published (not Web) sources, it should make appropriate use of direct quotations , and should include in-text citations (as either footnotes or endnotes). (25%)

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