21. 1220: Information From Answers.com The Arithmetica of jordanus nemorarius (aka Jordanus de Nemore) most likely b.Borgentreich (Germany), c. 1190, d. at sea, 1260 (some sources say February http://www.answers.com/topic/1220

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping In the year Construction The vault of the present cathedral at Chartres is completed. See also 1194 Construction 1240 Construction Materials The Dictionary of Jean de Garlande [b. 1190, d. 1255] mentions techniques for producing silk thread. See also ce Materials 1221 Tools Mathematics The Arithmetica of Jordanus Nemorarius (a.k.a. Jordanus de Nemore) [most likely b. Borgentreich (Germany), c. 1190, d. at sea, 1260 (some sources say February 13, 1237)], written about this time, uses letters as variables, instead of generalizing from specific numerical cases. Other mathematical works include Algorismus demonstratus ("algorithm demonstrated") and De numeris datis ("on given numbers"), collections of rules for solving problems. See also 1209 Mathematics Fibonacci publishes Practica geometriae which re-introduces Euclid's geometry and Greek trigonometry. See also 1202 Mathematics 1225 Mathematics Physics Robert Grosseteste writes De iride seu de iride et speculo ("what the rainbow is and why"). He is the first scholar since unidentified authors of Hellenic times to recognize correctly that refraction of light is the principal cause of the rainbow and that reflection of light also contributes to its formation. Although he experiments with mirrors and lenses, his work is still highly speculative, lacking the experimental and mathematical verification of later scientists.

22. 1260: Information From Answers.com includes a method for the trisection of an angle that is probably owed tojordanus nemorarius; in any case, it produces only an approximation. http://www.answers.com/topic/1260

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping In the year Communication Bartholomew of Messina translates Problemata by pseudo-Aristotle from Greek into Latin. See also 1240 Communication William of Moerbeke [b. c. 1215, d. 1286] starts translation of almost the complete works of Aristotle from Greek into Latin. He also translates Hippocrates, Hero of Alexandria, Alexander of Aphrodisias, and Simplicius. See also 1240 Communication 1270 Mathematics Materials The Book of Trades by Etienne Boileau [b. 1210, d. 1282] describes several techniques used in textile manufacture. See also 1280 Tools Mathematics A translation of Euclid's Elements by Johannes Campanus (a.k.a. Campanus of Novara) [b. Novara (Italy) 1220, d. Viterbo (Italy) 1296], published about this time, includes a method for the trisection of an angle that is probably owed to Jordanus Nemorarius; in any case, it produces only an approximation. Campanus's edition of Euclid becomes standard for the next 200 years. See also 1482 Mathematics Physician Taddeo Alderotti [b. Florence (Italy), 1223, d. Bologna (Italy), c. 1295] urges other physicians to read Galen, Hippocrates, and Avicenna, helping to bridge the gap between Greek and European medicine.

23. The Math Forum - Math Library - Golden Ratio/Fibonacci Learn about the lives of Fibonacci and other important mathematicians LeonardoFibonacci, Édouard Lucas, Jacques Binet, jordanus nemorarius. http://mathforum.org/library/topics/golden_ratio/

Browse and Search the Library Home Math Topics Arithmetic/Early Number Sense/About Numbers : Golden Ratio/Fibonacci Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Fibonacci Numbers and the Golden Section - Ron Knott Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio. more>> The Fibonacci Series - Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999 more>> Aesthetics, dynamic symmetry, equations, the Divine Proportion, the Fibonacci sequence, the Golden rectangle, logarithmic spirals, formulas, links to other MathSoft pages mentioning the Golden Mean, and print references. Also available as MathML more>> Golden Ratio, Fibonacci Sequence - Math Forum, Ask Dr. Math FAQ

24. Math Forum Electronic Newsletter learn about the lives of Fibonacci and other mathematicians (Edouard Lucas,Jacques Binet, jordanus nemorarius); and explore some applications of the http://mathforum.org/electronic.newsletter/mf.intnews4.38.html

Volume 4, Number 38 Back to Table of Contents Artlandia THE FIBONACCI SERIES Anderson, Frazier, Popendorf; ThinkQuest 1999 http://library.advanced.org/27890/ http://cctc.commnet.edu/lta/ http://www.artlandia.com/ A Mathematica-based application for artistic interpretation of data and creating mathematical and algorithmic art. The software provides a selection of tools for constructing geometrical objects from numerical arrays, distributing geometric shapes over the plane, and making and manipulating lattices and wallpaper patterns, as well as performing graphics operations and transformations. Algorithms attempt to balance the perfectly predictable and symmetric with the creative and random. The site includes a graphics gallery and display of user-created art. Artlandia requires Mathematica 3.0 or higher and is available for all platforms that run Mathematica. The student version can be purchased at a discount; see also Artlandia'sinteractive program, Kaleidoscope. http://www.artlandia.com/software/kaleidoscope/

25. Die Traktate De Proportionibus Von Jordanus Nemorarius And Translate this page Next Page Last Page Go to Page. Image version. Die Traktate De Proportionibusvon jordanus nemorarius and Campanus. Page 193. HLL BUSARD *. http://tidsskrift.kb.dk/centaurus/showtext.pl?indgang&ar_id=373

26. Die Traktate De Proportionibus Von Jordanus Nemorarius And Translate this page Last Page Go to Page. Image version. Die Traktate De Proportionibus von JordanusNemorarius and Campanus. Page 194. * Venlo, Herungerstraat 123, Niederlande. http://tidsskrift.kb.dk/centaurus/showtext.pl?ar_id=373&page=194

27. CHRONOLOGY OF MATHEMATICIANS -1100 CHOU-PEI -585 THALES OF MILETUS 1260 jordanus nemorarius ARITHMETICA. 1270 WILLIAM OF MOERBEKE TRANSLATION OFARCHIMEDES. 1274 DEATH OF NASIR EDDIN. 1303 CHU SHI KIE PASCAL TRIANGLE http://users.adelphia.net/~mathhomeworkhelp/timeline.html

CHRONOLOGY OF MATHEMATICIANS -1100 CHOU-PEI -585 THALES OF MILETUS: DEDUCTIVE GEOMETRY PYTHAGORAS : ARITHMETIC AND GEOMETRY -450 PARMENIDES: SPHERICAL EARTH -430 DEMOCRITUS -430 PHILOLAUS: ASTRONOMY -430 HIPPOCRATES OF CHIOS: ELEMENTS -428 ARCHYTAS -420 HIPPIAS: TRISECTRIX -360 EUDOXUS: PROPORTION AND EXHAUSTION -350 MENAECHMUS: CONIC SECTIONS -350 DINOSTRATUS: QUADRATRIX -335 EUDEMUS: HISTORY OF GEOMETRY -330 AUTOLYCUS: ON THE MOVING SPHERE -320 ARISTAEUS: CONICS EUCLID : THE ELEMENTS -260 ARISTARCHUS: HELIOCENTRIC ASTRONOMY -230 ERATOSTHENES: SIEVE -225 APOLLONIUS: CONICS -212 DEATH OF ARCHIMEDES -180 DIOCLES: CISSOID -180 NICOMEDES: CONCHOID -180 HYPSICLES: 360 DEGREE CIRCLE -150 PERSEUS: SPIRES -140 HIPPARCHUS: TRIGONOMETRY -60 GEMINUS: ON THE PARALLEL POSTULATE +75 HERON OF ALEXANDRIA 100 NICOMACHUS: ARITHMETICA 100 MENELAUS: SPHERICS 125 THEON OF SMYRNA: PLATONIC MATHEMATICS PTOLEMY : THE ALMAGEST 250 DIOPHANTUS: ARITHMETICA 320 PAPPUS: MATHEMATICAL COLLECTIONS 390 THEON OF ALEXANDRIA 415 DEATH OF HYPATIA 470 TSU CH'UNG-CHI: VALUE OF PI 476 ARYABHATA 485 DEATH OF PROCLUS 520 ANTHEMIUS OF TRALLES AND ISIDORE OF MILETUS 524 DEATH OF BOETHIUS 560 EUTOCIUS: COMMENTARIES ON ARCHIMEDES 628 BRAHMA-SPHUTA-SIDDHANTA 662 BISHOP SEBOKHT: HINDU NUMERALS 735 DEATH OF BEDE 775 HINDU WORKS TRANSLATED INTO ARABIC 830 AL-KHWARIZMI: ALGEBRA 901 DEATH OF THABIT IBN - QURRA 998 DEATH OF ABU'L - WEFA 1037 DEATH OF AVICENNA 1039 DEATH OF ALHAZEN

28. Griechischer Geist Aus Basler Pressen: Griechischer Geist Aus Basler Pressen: 2m 2mmr Anfang der Schrift von jordanus nemorarius. Vollansicht http://www.ub.unibas.ch/kadmos/gg/pic/gg0287_009_txt.htm

Griechischer Geist aus Basler Pressen GG 0287 2mmr: Anfang der Schrift von Jordanus Nemorarius.

29. GG 287 - Griechischer Geist Aus Basler Pressen Translate this page der lateinischen Übersetzung des Planisphaeriums des Ptolemaeus aus demArabischen, von Rudolf von Brügge. 2mmr Anfang der Schrift von jordanus nemorarius. http://www.ub.unibas.ch/kadmos/gg/hi/higg0287.htm

Frank Hieronymus: Griechischer Geist aus Basler Pressen GG 287 Sphaerae atque Astrorum coelestium ratio, (GG 142) bzw. 1535 (GG 303) des Ptolemaeus ebenfalls mit dem Kommentar Theons bezeugen, die (sie ist am 1. = November 1538 bei ihm erschienen (GG 278) [GG 37] , 1541) und Urbanus (Bolzanus: 1530, 1535, dann wieder 1539). Und vom griechischen Lexikon plane er schon wieder eine neue Ausgabe (1537, dann wieder 1539, 1541). Bibliothekskatalog IDS Signatur: Bc IV 36:1 Illustrationen Titelseite mit einer Kopie der Dionysius/Cleopatra-Einfassung Hans Holbeins vom Metallschneider CV von 1524. 1ar: Widmung Jacob Zieglers an Paulus Bombasius aus Bologna, 1. Seite (re). 1av: Widmung Jacob Zieglers, 2. Seite und Beginn der Beschreibung der Sphaera solida des Archimedes. 3cv: Anfang des griechisch-lateinischen Textes der Sphaera des "Proklos" (li); Scholien (re). ... 2mmr: Anfang der Schrift von Jordanus Nemorarius.

30. Medieval Mathematics Two Figures From The Later Middle Ages Figures like Jordanus de Nemore (referred to as either Jordanus or Nemorarius), strong likelihood that the works of another author, jordanus nemorarius, http://www.math.rutgers.edu/courses/436/Honors02/medieval.html

Medieval Mathematics: Two Figures from the Later Middle Ages Teresa Kuo Demonstratio de algorismo , which details the Arabic number system and its use of integers. Other treatises include the Demonstratio de minutiis, which covered fractions, and the Liber phylotegni de triangulis, wh ich highlighted geometric proofs [4, p. I182]. His work De numeris datis Let the given number be abc and let it be divided into two parts ab and c, and let d be the given product of the parts ab and c. Let the square of ab be e and let four times d be f, and let g be the result of taking f from e. Then g is the square of the difference between ab and c. Let h be the square root of g. Then h is the difference between ab and c. Since h is known, c and ab are determined [1, p. 284]. Nemorarius, unlike Euclid however, did not state that the variables were to be regarded as being line segments, but this was inferred. A different medieval mathematician credited with using Hindu-Arabic numerals was Leonardo de Pisa, a contemporary of Ne morarius. Leonardo de Pisa, (ca. 1180-1250), was born in Pisa (now part of Italy) and was the son of Guglielmo Bonaccio (from "Fibonacci", or "son of Bonaccio", is derived). This, and most information concerning the life of Fibonacci comes from an autobiographical passage in the beginning of the one of his works, the Liber Abbaci (a2 + b2)(c2+d2) = (ac + bd)2 + (bc - ad)2 = (ad + bc)2 + (ac - bd)2

31. TIMELINE 13th CENTURY Page Of ULTIMATE SCIENCE FICTION WEB GUIDE In this decade, jordanus nemorarius is the first to use letters to representalgebraic variables, as explained in his treatise, the Arithmetica. http://www.magicdragon.com/UltimateSF/timeline13.html

TIMELINE 13th CENTURY Return to Timeline Table of Contents Return to Ultimate SF Table of Contents TIMELINE 13th CENTURY May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge. We examine both works of fiction and important contemporaneous works on non-fiction which set the context for early Science Fiction and Fantasy. There are hotlinks here to authors, magazines, films, or television items elsewhere in the Ultimate Science Fiction Web Guide or beyond. Most recently updated: 13 Apr 2003 (48 expanded to 59 Kilobytes). It also utilizes facts from Volume I of D.E. Smith's " History of Mathematics " [(c) 1921 by David Eugene Smith; (c) 1951 by May Luse Smith; New York: Dover, 1958]. Arguably the best book on the century is " The Thirteenth, Greatest of Centuries " by J. J. Walsh [New York, 1907]. Executive Summary of the Century Major Books of the Decade 1200-1210 Major Books of the Decade 1210-1220 Major Books of the Decade 1220-1230 ... Where to Go for More : 51 Useful Reference Books Executive Summary of the 13th Century This Century marks the final flowering of Chivalry: Armored Knights on horseback, and the bloody Fourth through Eighth

32. References For Jordanus References for jordanus nemorarius. Biography Articles HLL Busard, TheArithmetica of jordanus nemorarius, in SS Demidov et al. (eds http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZAF5B.htm

33. Earliest Uses Of Symbols For Variables jordanus nemorarius (12251260) used letters to replace numbers. Christoff Rudolffused the letters a, c, and d to represent numbers, although not in http://members.aol.com/jeff570/variables.html

Earliest Uses of Symbols for Variables Last revision: Dec. 24, 2001 Greek letters. The use of letters to represent general numbers goes back to Greek antiquity. Aristotle frequently used single capital letters or two letters for the designation of magnitude or number (Cajori vol. 2, page 1). Diophantus (fl. about 250-275) used a Greek letter with an accent to represent an unknown. G. H. F. Nesselmann takes this symbol to be the final sigma and remarks that probably its selection was prompted by the fact that it was the only letter in the Greek alphabet which was not used in writing numbers. However, differing opinions exist (Cajori vol. 1, page 71). In 1463, Benedetto of Florence used the Greek letter rho for an unknown in Trattato di praticha d'arismetrica. (Franci and Rigatelli, p. 314) Roman letters. In Leonardo of Pisa's Liber abbaci (1202) the representation of given numbers by small letters is found. The Boncompagni edition, page 455, has: diuidatur aliquis numerus .a. in duas partes, que sint .b.g.; et diuidatur .a. per .b., et ueniet .e.; et .a. per .g. ueniet .d.: dico quod multiplicatio .d. in .e.est sicut agregatio .d.cum .e. [divide some number .a. in two parts which are .b.g.; and divide .a. by .b. to obtain .e.; and .a. by .g. to obtain .d.: I say that the product of .d. in .e. is as the sum of .d. with .e.] The dots were used to bring into prominence letters occurring in the running text, a practice common in manuscripts of that time [Barnabas Hughes; Cajori vol. 2, page 2].

34. PSIgate Timeline - Physics 631250 jordanus nemorarius makes advances in the field of medieval physics,particularly statics. 641269 Petrus de Marincourt describes a compass with a http://www.psigate.ac.uk/newsite/physics_timeline.html

35. PSIgate Timeline - Science From 1 - 1600 1250phys jordanus nemorarius makes advances in the field of medieval physics,particularly statics. 1252ast Alfonsine astronomical tables published; http://www.psigate.ac.uk/newsite/science_timeline2.html

36. References For Jordanus References for jordanus nemorarius. Version for printing Articles HLL Busard,The Arithmetica of jordanus nemorarius, in SS Demidov et al. http://www-groups.dcs.st-andrews.ac.uk/history/References/Jordanus.html

References for Jordanus Nemorarius Version for printing Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: H L L Busard, Jordanus de Nemore, 'De elementis arithmetice artis' : A medieval treatise on number theory. Parts I, II (Stuttgart, 1991). M Clagett, Archimedes in the Middle Ages (Madison, Wis., 1964). B B Hughes, Jordanus de Nemore, De numeris datis (Berkeley-Los Angeles-London, 1981). E A Moody and M Clagett (eds.), The medieval science of weights (Scientia de ponderibus), Treatises ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de Nemore, and Blasius of Parma (Madison, Wis., 1952). Articles: H L L Busard, The Arithmetica of Jordanus Nemorarius, in S S Demidov et al. (eds), Amphora : Festschrift for Hans Wussing on the occasion of his 65th birthday (Basel- Boston- Berlin, 1992), 121-132. H L L Busard, Die Traktate 'De Proportionibus' von Jordanus Nemorarius und Campanus, Centaurus J Hoyrup, Jordanus de Nemore, 13th Century Mathematical Innovator, Archive for History of Exact Science J Hoyrup, Jordanus de Nemore : a case study on 13th century mathematical innovation and failure in cultural context

37. ELEMENTARY PROBLEMS AND CHINESE MATHEMATICS In the Middle Ages in Europe, from the De Numeris Datis of jordanus nemorarius (1225 AD) as follow If there should be four munbers in proportion and http://www.mcs.csuhayward.edu/~malek/Mathlinks/Chinesemath.html

Vu Pham vvpham Presented 6/15/95 Received 6/5/95 ELEMENTARY PROBLEMS AND CHINESE MATHEMATICS 1) MATHEMATICAL RECREATIONS In the Middle Ages there developed a new form of puzzle problem, one suggested by the later Greek writers and modified by oriental influences. Problem of Metrodorus. So far as the Greek were concerned the source book for this material is the Greek Anthology. This contains the arithmetical puzzle, supposed to be due to Metrodorus about the year 500. Polycrates speaks : " Blessed Pythagoras ( c 540BC), Heliconian scoin of the Muses, answer my question: How many in thy house are engaged in the contest for wisdom performing excellently?" Pythagoras answers: " I will tell thee, then, Polycrates. Half of them are occupied with belles lettres; a quarter apply themselves to studying immortal nature; a seventh are all intent on silence and the eternal discourse of their hearts. There are also three women, and above the rest is Theano. That is the number of interpreters of the Muses I gather round me." The following problem relates to a statue of Pallas ( about the time of such Christian scholars as Capella and Cassiodorus, 460 AD and 502AD) lusty poets. Christians gave half of gold, Thespis one eighth, one tenth, and one twentieth, but the remaining nine talents and the workmanship are the gift of."

38. WebQuest:  Algebra Adventures In The Middle Ages jordanus nemorarius SCIPIONE DEL FERRO. NICOLE OF ORESME NICCOLO TARTAGLIA.REGIOMONTANUS GIROLAMO CARDANO. LUDOVICO FERRARI RAFAEL BOMBELLI. FRANCOIS VIETE http://michelle_sinclair.tripod.com/mes.htm

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Tripod Free Games Share This Page Report Abuse Edit your Site ... Next by Michelle Sinclair cLICK HERE TO e-MAIL ME back to index page INTRODUCTION tASK ... NOTES TO TEACHER (INCLUDES STANDARDS) Introduction The year is 3003. You have been selected by the government to be a part of a team of researchers to time travel to the past and study the beginnings of modern math. The time period of focus starts with the middle ages and continues through the Renaissance. This was the age of discovery complete with the growth of universities and the leadership of both a Pope and an Emperor. TASK Your team will be assigned a certain mathematician as your subject of research. Each team member with have tasks to fulfill and information to retrieve. Your results when you return will be presented to an audience of your peers and evaluated by them. The central question of your presentation is "How does this mathematician's algebra compare to our prior algebra studies?" Your team will also compile a portfolio to present your findings. Let's get started. Back to top PROCESS Each member of the team will play a different role. You select amongst yourselves to be a Mathematician, a Historian or a Teacher.

39. Physics Time-Line To 1799 1225 jordanus nemorarius, mechanics of lever and composition of motion 1250Albertus Magnus, isolation of arsenic 1260 Roger Bacon, empiricism http://www.cartage.org.lb/en/themes/Sciences/Physics/aboutphysics/physicstimelin

Themes Science Physics About Physics, Generalities ... Physics Time-Line Physics Time-Line to 1799 Nicolaus Copernicus Thales of Miletus , prediction of an eclipse Thales of Miletus , birth of scientific thought Thales of Miletus , water as the basic element Thales of Miletus , magnets and attraction to rubbed amber Thales of Miletus , first cosmologies Anaximenes , flat Earth Pythagoras , understanding the world and mathematics Anaximander , Earth surface is curved (cylinder) Parmenides , paradoxes of change and motion Pythagoreans , Earth is a sphere Oenopides , finds angle of Earth's tilt to ecliptic Protagoras , reality comes from the senses Heraclitus , fire as primary substance Heraclitus , change is the essence of being Parmenides , Earth is a sphere Anaxagoras , materials are made of "seeds" (atoms) Anaxagoras , sun, moon and stars are made of same material as Earth Anaxagoras , sun as a hot glowing rock Eudoxus , Celestial spheres Empedocles , Four elements: Earth, Air, Fire and Water Philolaus , Earth Rotates Zeno , paradoxes of discrete or continuous space and time Leucippus , indivisble atoms Democritus , Atomic theory Plato , theory of knowledge Plato , ether as a fifth element Democritus , Milky Way is composed of many stars Aristotle , Free falling bodies accelerate but heavier bodies fall faster Heracleides , Venus and Mercury orbit the sun Chinese , recorded observation of a supernova Heracleides , Rotation of the Earth Aristotle , Earth is a sphere Aristotle

40. Math History - Middle Ages About 1225, jordanus nemorarius writes on astronomy. In mathematics he usesletters in an early form of algebraic notation. http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MmiddleAges.htm

Math History Timeline Middle Ages 500 - 1400 A.D. Math History Prehistory and Ancient Times Middle Ages Renaissance Reformation ... 20th Century ... non-Math History Prehistory and Ancient Times Middle Ages Renaissance Reformation ... External Resources Varahamihira produces Pancasiddhantika (The Five Astronomical Canons). He makes important contributions to trigonometry. Decimal notation is used for numbers in India. This is the system on which our current notation is based. Brahmagupta writes Brahmasphutasiddanta (The Opening of the Universe), a work on astronomy; on mathematics. He uses zero and negative numbers, gives methods to solve quadratic equations, sum series, and compute square roots. About 700 Mathematicians in the Mayan civilization introduce a symbol for zero into their number system. About 810 Al-Khwarizmi writes important works on arithmetic, algebra, geography, and astronomy. In particular Hisab al-jabr w'al-muqabala (Calculation by Completion and Balancing)

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