21. The Birth Of Algebra In Germany, christoff rudolff (1499 1555) wrote a book in 1525 called simply Coss.The Italian algebraists had identified the unknown value in a problem http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html

The Birth of Algebra Introduction: Bridging a millenium In the year AD 312, on the eve of a battle against would-be rivals for the Roman Imperial throne, Constantine had a dream that instructed him to place the chi rho , the Christian symbol formed by superimposing the first two letters of the Greek name Christos , on the shields of his soldiers. When he won the battle and became Emperor, he issued an edict of tolerance for Christian believers. Later, on his deathbed, Constantine himself became a Christian, placing it in a position of prominence in the Empire from which it would influence the history of the Western world to this day. In 324, Constantine moved the seat of the Empire to the Greek town of Byzantium in the east of the empire, renaming it Constantinople after himself. His was one of the last strong governments of the Roman Empire. The tenuous union of the eastern and western halves of the empire during the fourth century continued to fray, so that by the year 400 it had split in two for good. The Goths entered Rome in 476 , bringing down the Western Empire. This marks the start of the Middle Ages, when Greek culture was effectively cut off from the West. Tribal governments held sway, giving way to feudal society and the slow development over centuries of what would eventually become the familiar nation-states of Europe.

22. Part II Outline examples of this development appear in France in the work of Nicholas Chuquet,in Germany by christoff rudolff, and in England by Robert Recorde. http://cerebro.xu.edu/math/math147/02f/part2/part2.html

MATH 147 Part II Outline Ptolemy Greek astronomers inherited much of their astronomy from the Babylonians. Beginning with Aristarchus (4th c.) and Eratosthenes (3rd c.), however, they looked at the cosmos as being described by geometric patterns (spherical motions) that could be recorded, measured, and predicted, rather than simply the will of the gods. Eudoxus (4th c.) developed a geocentric model that placed the earth at the fixed center of the universe. This homocentric version posited concentric spheres on which the seven planets (Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn) traveled around the earth. Apollonius (3rd c.) refined this to an eccentric model which assumed that the planetary spheres did not share the same center. This accounted for variability in brightness of the planets. Hipparchus (2nd c.) prepared the first table of chords to assist with astronomical calculation. For this he is called "the father of trigonometry". The chord of an angle is related to the modern-day sine of the angle by crd a = 2 sin a Claudius Ptolemy (2nd c. AD) wrote the

23. Origins Of Some Arithmetic Terms-4 According to Jeff Miller s web site, The radical symbol first appeared in 1525in Die Coss by christoff rudolff (14991545). http://www.pballew.net/arithme4.html

Math Words, pg 4 Back to Math Words Alphabetical Index Add / Addition The arithmetic word add is from the Latin root addere , to give or to do. The dere part of the root is the same root that gives us Data/Datum and the name for dice . Donation and condone also share the same root. The first recorded use of the word in English is from "The Crafte of Nombrynge" according to Jeff Miller's web site . The document was one of the first English language documents dealing with mathematics. The symbol "+" for addition was used for surplus and deficit before it was used as an operation symbol. It has been shown that the symbol was used on barrels to mark them as over or under weight prior to the earliest known use in manuscripts. Some even suggest it dates back to the Early Greeks, but others suggest it is a short form of the script word et , Latin for and. The symbol seems to have been first used for an operation in the late 1400's and only came into common usage after it was used by Robert Recorde in his 1557 book, The Whetstone of Witte Altitude is the geometric name for the perpendicular distance from one base of a geometric figure to the opposite vertex, or parallel face. The word altitude is also sometimes used for the line segment representing this distance in a figure. The word comes from the Latin

24. Rudolff, Christoff Translate this page rudolff, christoff. rudolff, christoff, * 1500 (?) Jauer (Jawor, Polen), †1545 Wien, Mathematiker. Schüler von Grammateus in Wien. http://www.allaboutaustria.at:81/aeiou.encyclop.r/r935986.htm

A B C D ... Rottmeyer, Franz Robert - Rudolff, Christoff Rudolff, Christoff Rudolff, Christoff, * 1500 (?) Jauer (Jawor, Polen Band Allgemeine Deutsche Biographie Hinweise zum Lexikon

25. History Of Mathematics: Chronology Of Mathematicians Philip Schwartzerd (Melanchthon) (14971560); Andrias Osiander (1498-1552) *W;William Buckley (dc 1550); christoff rudolff (c. 1500-c. 1545) *SB *MT *W http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

26. TIMELINE 16th CENTURY Page Of ULTIMATE SCIENCE FICTION WEB GUIDE by Cuthbert Turnstall 1525 Die Coss by christoff rudolff, one of the firstbook to use decimals, introduces the modern symbol for square roots. http://www.magicdragon.com/UltimateSF/timeline16.html

TIMELINE 16th CENTURY Return to Timeline Table of Contents Return to Ultimate SF Table of Contents TIMELINE 16th CENTURY May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge. What were Ariosto and Cyrano doing on the Moon, and how did they get there? 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. Over 58 kilobytes in length. Most recently updated: 24 December 2003 16th Century Executive Summary of the Century Major Books of the Decade 1500-1510 Major Books of the Decade 1510-1520 Major Books of the Decade 1520-1530 ... Where to Go for More : 51 Useful Reference Books Executive Summary of the Century The 16th Century was a time of great exploration, religious turmoil, political turmoil, scientific advances, and extraordinary literature. EXPLORATION Ferdinand Magellan 's expedition circumnavigated the world. He himself died on the mission, which started 1519. The only surviving ship to return was that commanded by Basque captain

27. La Page Des Mathematiques Au Lycee Claude Fauriel, Classes Preparatoires, Saint Translate this page christoff rudolff (1499-1545) introduit le symbole pour désigner la racine carrée.François Viète (1540-1603) polynôme. http://mathematiques.fauriel.org/doc-mots.html

Accueil Autres disciplines Accueil MP ... Documents Les mots mathématiques et transcendant aux mots et fonction nombres impossibles nombres imaginaires nombres imaginaires nombres complexes touchantes sont devenues des tangentes . Les fluxions , et les fonctions synectiques holomorphes squelette , de ossuaire murs , des appartements et des immeubles ... Charles Ehresmann, inventeur des mots : fibre, jet, germe, tige injection injectif en 1952 dans les Foundations of algebraic topology surjectif surjection en 1964 dans les Foundations of algebraic topology bijection biunivoque n mots En tout bien tout honneur... Tout commence avec : Pythagore (580-520 av. J C) Pythagoriciens classification des nombres : nombres pairs, impairs, impair-pair, nombres pairement pairs (puissances de 2), pair-impair (i.e. de la forme 2(2m+1)), impair-pair (i.e. de la forme 2 n+1 : puissance : logique. Euclide (365-300 av. J C) oper edei deiksai q.e.d., quod erat demonstrandum, : arbelos. Apollonios de Perge (262-190 av JC) : ellipse, parabole et hyperbole, cylindre, asymptote (probablement) Al Khowarizmi (790-850) Fibonacci (1170-1250) : addition, extraction (1201

28. Lesson Six A German mathematician named christoff rudolff who first used it in 1525 inventedit. As a result of the previous definitions we can list of the following http://www.personal.psu.edu/faculty/j/x/jxt18/Math21_WEB/Lesson6/lesson_six.htm

29. La Radicación - Naveguitos Translate this page Un dato interesante Un matemático alemán llamado christoff rudolff fue quienempleó por primera vez el símbolo actual de la raíz cuadrada. http://www.naveguitos.com.ar/comun/v2/vis_17568.asp

Juegos!! Juegos!! Juegos!! Escuadrón del Conocimiento> Matemática Números y operaciones La radicación document.write(""); La radicación document.write(""); La radicación es la operación inversa de la potenciación . Veamos un ejemplo: Mediante la potenciación podemos calcular que 3 ³ = 27 Ahora nos preguntamos: ¿Qué número multiplicado por sí mismo 3 veces (es decir elevado al cubo) da 27? Esta pregunta se escribe así: ³V¯27 = (Este es el número que da como resultado) La operación se llama RADICACIÓN y se lee así: la raíz cúbica de 27 es 3. Tomando el ejemplo anterior, veamos ahora cuáles son los elementos de una raíz: ³V¯27 = 3 es el índice es el radicando El resultado es la raíz V¯es el símbolo o signo radical Un dato interesante : Un matemático alemán llamado Christoff Rudolff fue quien empleó por primera vez el símbolo actual de la raíz cuadrada. Esto ocurrió en el año 1525. A continuación te detallamos algunos ejemplos: ³V¯125 = 5 Porque 5³ = 125 ³V¯64 = 4 Porque 4³ = 64 V¯81 = 3 Porque 3 Recomendá esta nota a un amigo Escuadrón del Conocimiento> Matemática Números y operaciones La radicación

30. Untitled Document christoff rudolff Culture German Area of Study Mathematics Century 16Contribution In his book Die Cross, he introduces a version of the modern symbol http://library.thinkquest.org/C008444/pages/library/info/european.html

European Scientists Eutocius Culture:Greek or Roman Area of Study:mathematics Century:6 Contribution: writes commectaries on the aorks of Archimedes and Apollonius; they remain the best source of certain of their mathematics. Gerbert Culture: French Area of Study: Mathematics Century:10 Contribution: This churchman introduces the abacus to Europe, although the new method for writing numbers does not catch on; he seems to have been unaware of 0. Abbe Suger Culture: English Area of Study:technology Century:12 Contribution: Starts construction ont he abbey church of St. Denis, the first Gothic Church with flying buttresses. Adelard of Bath Culture: European Area of Study:Astronomy Century:12 Contribution: He translates "Astronomical tables" by Al-Khowarizmi from the Arabic in 1126; anout this time he also translate Al-Khowazrimi's "Liber ysagogarum alchorismi, a work about arithmetic. He also translates Euclid's Elements (15 Books, of which 13 are now believed to be geniune) from the Arabic in 1142.

31. Raiz Quadrada - Matemática.com.prazer Translate this page da autoria de christoff rudolff (1499-1545), porém sem índices que Este símbolo criado por rudolff não teve aceitação imediata nem mesmo na Alemanha http://www.geocities.com/matematicacomprazer/raizquadrada.html

Raiz Quadrada O símbolo de raiz apareceu pela primeira vez em 1525 no livro de álgebra Die Cross , da autoria de CHRISTOFF RUDOLFF (1499-1545), porém sem índices que indicassem a natureza da raiz (ou seja, se era raiz quadrada, cúbica, de quarta potência...). O símbolo (sem o travessão) pode ter sido usado por se parecer com a forma manuscrita do r da palavra radix , ou pode ter mesmo sido uma invenção arbitrária. Este símbolo criado por RUDOLFF não teve aceitação imediata nem mesmo na Alemanha, sua terra natal. A letra l (do latim latus , lado) era muita vezes utilizada. Assim l 4 representava Em 1655 JOHN WALLIS usou o índice de raiz quadrada da mesma forma que utilizamos hoje: para o conhecido x Para retornar ao início desta página MAIS matemática.com.prazer! Ano 0, 2000 Márcio Nascimento Todos os Direitos Reservados para a Educação do Brasil Última Modificação em 28/02/2000

32. Flas Matemático Translate this page El símbolo de la raíz, aparece por primera vez en el libro de álgebra publicadoen alemán en 1525, de christoff rudolff. http://www.geocities.com/Athens/Acropolis/4329/flas.htm

MIDI: "Yellow River" de Tony Chistie Coordenadas cartesianas Los Elementos de Euclides Letras de cambio Los quilates de una joya ... Ruffini y su regla Las coordenadas cartesianas Los cero La El tiene su origen en una r inicial de la palabra latina radix. Los Elementos indios Los Parece ser que las letras de cambio Cuando decimos que un objeto de oro tiene 16 quilates , significa que de 24 partes del objeto, 16 son de oro. Sirve para medir la ley; en este caso el objeto de oro tiene una ley de 16 quilates. El origen de los signos + y - El signo = para las igualdades fue utilizado por primera vez por el inglés Robert Recorbe en 1557 apareciendo por primera vez en su libro "El aguzador del ingenio", siendo el primer tratado inglés de álgebra. Según el autor, eligió ese símbolo porque dos cosas no pueden ser más iguales que dos rectas paralelas. trascendente La regla de los signos + por + da + - por - da + - por + da - + por - da - La divisibilidad por 2, 5, 3 y 9

33. List Of Scientists By Field Translate this page rudolff, christoff. Rudolphi, Karl Asmund. Rudolphi, Karl Asmund. Ruedemann, Rudolf.Ruedemann, Rudolf. Ruel, Jean. Ruel, Jean. Ruffer, Marc Armand http://www.indiana.edu/~newdsb/r.html

Rabl, Cari Rabl, Cari Rademacher, Hans Radon, Johann Raffles, Thomas Stamford Bingley Rafinesque, Constantine Samuel Raman, Chandrasekhara Venkata Raman, Chandrasekhara Venkata Ramanujan, Srinivasa Aaiyangar Rames, Jean Baptiste Rames, Jean Baptiste Rammelsberg, Karl Ramon, Gaston Ramsauer, Carl Wilhelm Ramsay, Andrew Crombie Ramsay, William Ramsdell, Lewis Stephen Ramsdell, Lewis Stephen Ramsdell, Lewis Stephen Ramsden, Jesse Ramsey, Frank Plumpton Ramus, Peter Ramus, Peter Ramus, Peter Rankine, Alexander Oliver Rankine, Alexander Oliver Rankine, William John Macquorn Rankine, William John Macquorn Ranvier, Louis-Antoine Ranyard, Arthur Cowper Raspe, Rudolf Erich Raspe, Rudolf Erich Rateau, Auguste Camille Edmond Rateau, Auguste Camille Edmond Rathke, Martin Heinrich Rathke, Martin Heinrich Ratzel, Friedrich Ratzel, Friedrich Ratzel, Friedrich Raulin, Jules Rauwolf, Leonhard Ray, John Ray, Prafulla Chandra Rayet, Georges Antoine Pons Raymond of Marseilles Raymond, Percy Edward Raymond, Percy Edward Razmadze, Andrei Mikhailovich Ra Reck, Hans Reck, Hans

34. New Dictionary Of Scientific Biography Translate this page rudolff, christoff Ruffini, Paolo Rumovsky, Stepan Yakolevich Runge, Carl DavidTolmé Russell, Bertrand Arthur William Rydberg, Johannes Saccheri, Girolamo http://www.indiana.edu/~newdsb/math.html

Make Suggestions Mathematics Abel, Niels Henrik Abraham Bar ?iyya Ha-Nasi Abu Kamil Shuja? Ibn Aslam Ibn Mu?ammad Ibn Shuja? Abu'l-Wafa? al-Buzjani, Mu?ammad Ibn Mu?ammad Ibn Ya?ya Ibn Isma?il Ibn al- ?Abbas Adams, John Couch Adelard of Bath Adrain, Robert Aepinus, Franz Ulrich Theodosius Agnesi, Maria Gaetana Aguilon, François d' A?mad Ibn Yusuf Aida Yasuaki Ajima Naonobu Akhiezer, Naum Il'ich Albert, Abraham Adrian Albert of Saxony Alberti, Leone Battista Aleksandrov, Pavel Sergeevich Alembert, Jean Le Rond d' Alzate y Ramírez, José Antonio Ampère, André-Marie Amsler, Jakob Anatolius of Alexandria Anderson, Oskar Johann Viktor Andoyer, Henri Angeli, Stefano Degli Anthemius of Tralles Antiphon Apollonius of Perga Appell, Paul Arbogast, Louis François Antoine Arbuthnot, John Archimedes Archytas of Tarentum Argand, Jean Robert Aristaeus Aristarchus of Samos Arnauld, Antoine Aronhold, Siegfried Heinrich Artin, Emil Atwood, George Autolycus of Pitane Auzout, Adrien

35. References For Rudolff References for christoff rudolff. Biography in Dictionary of ScientificBiography (New York 19701990). Books W Kaunzner, Über http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/References/Rudo

36. Short Biographies Rh of Euler. rudolff, christoff 1499 1545 Austrian His book Coss , writtenin 1525, is the first German algebra book. The reason http://www.grammar.net.nz/dept_html/dept_common/scotch_college/maths/Rh.htm

37. Untitled Document Gregorio (18531925) Richter, Charles F. (1900-1985) Riemann, George (1826-1866)Rolle, Michel (1652-1719) rudolff, christoff (1499-1545) Ruffini, Paolo (1765 http://colliervillehs.scs.k12.tn.us:16080/~holmesm/ExtraCreditNames.html

NAME OF MATHEMATICIAN Abbe, Ernst (1840-1905) Abel - Niels Henrik Abel (1802-1829) Agnesi, Maria (1755-1842) Ahmes (1680 B.C.-1620 B.C.) Aiken, Howard (1900-1973) al-Kashi, Jamshid (about 1430) Al-Khowarizmi, Muhammed ibn Musa (780-850) Apollonius of Perga (262 B.C.-190 B.C.) Archimedes of Syracuse (287 B.C.-212 B.C.) Archytas of Taretum (428 B.C.-350 B.C.) Argand, Jean-Robert (1768-1822) Aristotle (384 B.C.-322 B.C.) Aryabhata (476-550) Babbage, Charles (1792-1871) Baire, Rene (1874-1932) Banneker, Benjamin (1731-1806) Bell, Eric Temple (1883-1960) Beltrami, Eugenio (1835-1899) Bernouli, Daniel (1760-1782) Bernoulli, Jaque (1655-1705) Bernoulli, Johann (1667-1748) Bhaskara (1114-1185) Bolyai, Janos (1802-1860) Bonaparte, Napoleon (1778-1846) Boole, George (1815-1864) Borel, Felix Edouard (1871-1956) Brahe, Tycho (1546-1601) Brahmagupta (598-670) Briggs, Henry (1561-1630) Brouncker, Lord William (1620-1684) Brouwer, Luitzen E. J. (1881-1967) Buffon, Comte George (1707-1788)

38. Famous Mathematicians With An R Edward Routh Mary Rudin Ferdinand Rudio christoff rudolff Paolo Ruffini CarleRunge Bertrand Russell John Russell Daniel E. Rutherford Johannes Rydberg http://www.famousmathematician.com/az/mathematician_R.htm

Mathematicians - R Hans Rademacher Richard Rado Tibor Rado Johann Radon Johann Rahn Cadambathur Rajagopal Chidambaram Ramanujam Srinivasa Ramanujan Jesse Ramsden Frank Ramsey Peter Ramus Robert Rankin William Rankine Joseph Raphson Helena Rasiowa Andrei Razmadze Robert Recorde Mina Rees Hans Reichenbach Kurt Reidemeister Irving Reiner Robert Remak Evgeny Remez Julio Rey Pastor Theodor Reye Paul du Bois-Reymond Antoine-Andre Reynaud Charles Reyneau Osborne Reynolds Georges de Rham Georg Joachim Rheticus Vincenzo Riccati Matteo Ricci Michelangelo Ricci Georgorio Ricci-Curbastro Jules Richard Louis Richard Lewis Richardson Jean Richer Herbert Richmond G.F. Bernhard Riemann

39. UB Bielefeld: Christoff Rudolff: Die Coss Christoffs Rudolffs (Digitale Rekonstr Translate this page christoff rudolff Die Coss christoffs rudolffs. christoff rudolff Die Cosschristoffs rudolffs. http://www.ub.uni-bielefeld.de/diglib/rechenbuecher/coss/

Christoff Rudolff: Die Coss Christoffs Rudolffs

40. UB Bielefeld: Mitteilungen Der Bibliothek (Ausgabe 4 / 2005) Translate this page christoff rudolff Die Coss christoffs rudolffs (1553) http//www.ub.uni-bielefeld.de/diglib/rechenbuecher/coss/ Die Sammlung digitaler Drucke wird http://www.ub.uni-bielefeld.de/news/2005/2005_4.htm

Mitteilungen der Bibliothek, Ausgabe 4 / 2005 Ausgabe 4 / 2005 Universität Bielefeld als Vorreiter für "Open Access" Besondere Ruhezonen in der Bibliothek Datenbanken, digitale Texte und elektronische Zeitschriften ... www.ub.uni-bielefeld.de 1. Universität Bielefeld als Vorreiter für "Open Access" an deutschen Hochschulen I. Das Rektorat der Universität Bielefeld fordert die wissenschaftlichen Autoren der Universität nachdrücklich auf, alle veröffentlichten, wissenschaftlich referierten Artikel (sog. "Postprint-Versionen") als Kopie auf dem wissenschaftlichen Publikationenserver (e-Scholarship Repository) der Universität abzulegen, soweit rechtliche Bedenken der Verlage nicht entgegenstehen. Dies betrifft die Publikationen einer großen Zahl von Verlagen, die dieser "Selbst-Archivierung" durch Autoren an ihren Institutionen mittlerweile zustimmen. http://www.uni-bielefeld.de/ub/wp/bielefeld.htm Folgende DFG-geförderte Datenbanken haben wir bereits in unser Angebot "Datenbanken von A-Z" eingebunden: Periodicals Contents Index World Biographical Information System Declassified Documents Reference System Digital National Security Archive Early American Imprints Early English Books Online 18th century collection online Acta Sanctorum Europa Sacra Library of Christian Latin Texts Ut per litteras apostolicas Comintern Online Database Making of Modern Law China Academic Journals Aristoteles Latinus Database

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