1. Rudolff Christoff Rudolff. Born 1499 in Christoff Rudolff studied algebra atthe University of Vienna, between 1517 and 1521. He remained in http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Rudolff.html

Christoff Rudolff Born: 1499 in Jauer, Silesia (now Jawor, Poland) Died: 1545 in Vienna, Austria Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Christoff Rudolff studied algebra at the University of Vienna, between 1517 and 1521. He remained in Vienna after studying at the university and earned his living giving private lessons in mathematics. He did use the facilities offered by the university, being able to use books in the university library and talking with academics at the university. Rudolff's book Coss , written in 1525, is the first German algebra book. The reason for the title is that cosa is a thing which was used for the unknown. Algebraists were called cossists , and algebra the cossic art , for many years. Rudolff calculated with polynomials with rational and irrational coefficients and was aware that ax b cx has 2 roots. He used for square roots (the first to use this notation) and for cube roots and for 4 th roots. He has the idea that x = 1 which is important.

2. Biography-center - Letter R uk.asp?PAR_I_ID=10427. rudolff, christoff. wwwhistory.mcs.st-and.ac.uk/~history/ Mathematicians/rudolff.html. Rudomine, Albert http://www.biography-center.com/r.html

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3. Earliest Uses Of Symbols For Fractions In 1530, christoff rudolff (1499?1545?) used a vertical bar exactly as we use a decimal point today work seems to have been christoff rudolff, whose Exempel Büchlin appeared at http://members.aol.com/jeff570/fractions.html

Earliest Uses of Symbols for Fractions Last revision: Mar. 4, 2004 Earliest notations for fractions. The Babylonians wrote numbers in a system which was almost a place-value (positional) system, using base 60 rather than base 10. Their place value system of notation made it easy to write fractions. The numeral has been found on an old Babylonian tablet from the Yale collection. It is an approximation for the square root of two. The symbols are 1, 24, 51, and 10. Because the Babylonians used a base 60, or sexagesimal, system, this number is 1 x 60 + 24 x 60 + 51 x 60 + 10 x 60 , or about 1.414222. The Babylonian system of numeration was not a pure positional system because of the absence of a symbol for zero. In the older tablets, a space was placed in the appropriate place in the numeral; in some later tablets, a symbol for zero does appear but in the tablets which have been discovered, this symbol only used between other symbols and never in a terminal position. The earliest Egyptian and Greek fractions were usually unit fractions (having a numerator of 1), so that the fraction was shown simply by writing a numeral with a mark above or to the right indicating that the numeral was the denominator of a fraction. Ancient Rome.

4. Raiz Quadrada - Matemática.com.prazer de álgebra Die Cross, da autoria de christoff rudolff (14991545), porém sem índices que indicassem a Este símbolo criado por rudolff não teve aceitação imediata nem mesmo na 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

5. Rudolff [Rudolf], Christoff rudolff Rudolf, christoff. Note the creators of the Galileo Project and this catalogue cannot answer email on http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/rudolff.html

Catalog of the Scientific Community Rudolff [Rudolf], Christoff Note: the creators of the Galileo Project and this catalogue cannot answer email on genealogical questions. 1. Dates Born: fl Died: Dateinfo: Dates Certain Lifespan: 2. Father Occupation: Unknown No information on financial status. 3. Nationality Birth: Jauer, Silesia [now Poland] Career: Vienna, Austria Death: Vienna, Austria 4. Education Schooling: Vienna He learned algebra from Grammateus at the University of Vienna, probably some time between 1517 and 1521. With information so sketchy, anything is possible, but no degree is mentioned. 5. Religion Affiliation: Catholic (assumed). 6. Scientific Disciplines Primary: Mathematics 7. Means of Support Primary: Schoolmastering In Vienna, he supported himself by giving private lessons. Though not affiliated with the university, he was able to use its library. 8. Patronage Type: Eccesiastic Official He dedicated his Coss (1525) to the Bishop of Brixen (now Bressanone, Italy). 9. Technological Involvement Type: Applied Mathematics His Künstliche Rechnung mit der Ziffer und mit den Zahlpfennigen (1526) contains an "Exempelbüchlein" which contains examples of the use of mathematics in commerce and manufacturing.

6. References For Rudolff References for christoff rudolff. Biography in Dictionary of ScientificBiography (New York 19701990). Books W Kaunzner, Über http://www-gap.dcs.st-and.ac.uk/~history/References/Rudolff.html

References for Christoff Rudolff Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: Ein Beitrag zur Geschichte der Rechenkunst zu Beginn der Neuzeit (Munich, 1970). Articles: M Cantor, II (Leipzig, 1913), 397-399, 425-429. M Terquem, Christophe Rudolff, Annali di scienze matematiche e fisiche 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/Rudolff.html

7. Rudolff Biography of christoff rudolff (14991545) christoff rudolff. Born 1499 in Jauer, Silesia (now Jawor, Poland) christoff rudolff studied algebra at the University of Vienna, between 1517 and http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Rudolff.html

Christoff Rudolff Born: 1499 in Jauer, Silesia (now Jawor, Poland) Died: 1545 in Vienna, Austria Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Christoff Rudolff studied algebra at the University of Vienna, between 1517 and 1521. He remained in Vienna after studying at the university and earned his living giving private lessons in mathematics. He did use the facilities offered by the university, being able to use books in the university library and talking with academics at the university. Rudolff's book Coss , written in 1525, is the first German algebra book. The reason for the title is that cosa is a thing which was used for the unknown. Algebraists were called cossists , and algebra the cossic art , for many years. Rudolff calculated with polynomials with rational and irrational coefficients and was aware that ax b cx has 2 roots. He used for square roots (the first to use this notation) and for cube roots and for 4 th roots. He has the idea that x = 1 which is important.

8. Rottmeyer, Franz Robert - Rudolff, Christoff Translate this page Rottmeyer, Franz Robert - rudolff, christoff. Rottmeyer, Franz Robert. Rotunde. Rudolf,Leopold. rudolff, christoff. Hinweise zum Lexikon Abkürzungen im Lexikon. http://www.aeiou.at/aeiou.encyclop.r.r24

A B C D ... Rudolfinische Hausordnung - Ruprecht, Heiliger Wählen Sie das gewünschte Stichwort in der nachfolgenden Liste. Rottmeyer, Franz Robert - Rudolff, Christoff Rottmeyer, Franz Robert Rotunde Rubatscher, Maria Veronika Rubin, Marcel ... Hinweise zum Lexikon

9. Rudolff, Christoff Translate this page Rottmeyer, Franz Robert - rudolff, christoff (25/25). Rudolf, Leopold, Rottmeyer,Franz Robert - rudolff, christoff. rudolff, christoff. http://www.aeiou.at/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 Suche nach hierher verweisenden Seiten

10. Ask Jeeves For Kids! Saccheri, Giovanni. rudolff, christoff. Roomen, Adriaan van. Rolle, Michel http://www.ajkids.com/kidsaskjeeves.asp?ask=Galileo&qSource=0&origin=0&a

11. Bayerische Staatsbibliothek - Förderverein Translate this page rudolff, christoff Künstliche rechnung mit der Ziffer und mit den zal pfennigensampt der Wellischen Practica und allerley fortheyl auff die Regel De Tri. http://www.bsb-muenchen.de/foerder/p484.htm

Zur Homepage Signatur: Res. Math.p. 484 Deckel gebrochen "Exempelbuch" webmaster@bsb-muenchen.de < /font>

12. Bayerische Staatsbibliothek - Förderverein Translate this page rudolff, christoff Künstliche rechnung mit der Ziffer und mit den zal pfennigensampt der Wellischen Practica und allerley fortheyl auff die Regel De Tri. http://www.bsb-muenchen.de/foerder/fhilf01.htm

Zur Homepage Buchpaten und Spender der Jahre Die Buchpaten des Jahres 2001: spendeten Barbara Baum Dr. Georg Ostermaier Josef Rumpl , Rosenheim Dr. Albert Dietl Bernhard Eibl David Fuchs , Deggenhausen Buchbinderei Hertle Dr. Lothar Marx Margit Albrecht Karlheinz Boos , Konstanz Georg Demmel , Deisenhofen Dr. Wolfgang Grillo , Breitbrunn Monika Hierl Claudia Hildebrand E. Holzheid , Ingolstadt Peter Konetschy , Niedereschach Elisabeth Lindinger , Neuburg a.d.D. Baldung Schreiner Anita und Gerhard Stadlbauer , Bonbruck Anton Suppmann , Landsberg a. Lech Theresia Zeller Titel eigener Wahl entschieden sich aus Gilching Brunstemann, Friedrich: Die Geschichte der Kleinen oder St. Johannis-Gilde in Wort und Bild. - 1902 Signatur: 38.2793 Szabo, M. E.: Algebra of proofs. - 1978 Signatur: Z 72.718-88 Bernardinus de Busti: Rosarium sermonum Venedig: Georgius de Arrivabene, 16. August 1498 Signatur: 4 Inc.c.a.1485-2 Signatur: Bavar. 4358 y Geibel, Emanuel: Juniuslieder. - 1851. Signatur: P.o.germ. 430 tb Laurent, Michel: Histoire du football en Lorraine. - 1971 Signatur: 88.3647

13. ThinkQuest : Library : Go Forth & Multiply: A Mathematics Adventure A brief overview of the history and development of algebra. Nicolas Chuquet of France and christoff rudolff of Germany both developed systems of exponential notation. rudolff also noted that multiplication of powers corresponded http://library.thinkquest.org/C0110248/algebra/history2.htm

Index Education Want to learn more about the world of mathematics? Then go forth, and enter the wildest math adventure you've ever been! Learn new math concepts and refresh your knowledge for those you've already known. Understand how the formulae you use were derived from. Or, you can take a step back into the past and read about how mathematics and its concepts originated. Go forth and multiply! Visit Site 2001 ThinkQuest Internet Challenge Awards Achievement Award Students Teow Lim Raffles Junior College, Singapore, Singapore Vee San Raffles Girls' School (Secondary), Singapore, Singapore Coaches Poh Kheng Pioneer Junior College, Singapore, Singapore Jee Wah Raffles Girls' School (Sec), Hougang, Singapore Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

14. Hrvatska Akademija Znanosti I Umjetnosti. Knjižnica rodendanu. Kazalo. * Gaj, Ljudevit (hrv. preporoditelj i književnik; 1809-1872) * rudolff, christoff * Povijesna znanost. Pomocne http://161.53.55.45/HAZU-POV/per/Listici/b019349h.htm

Sign.: P 102 Zbornik Historijskog instituta Jugoslavenske akademije znanosti i umjetnosti. Vol. 7(1974) / urednici Marko Kostrenèiæ ; Grga Novak ; Zlatko Herkov. - 332 str., V : ilustr. Zbornik je posveæen akademiku Marku Kostrenèiæu o njegovu 90. roðendanu. - Kazalo. * Gaj, Ljudevit (hrv. preporoditelj i književnik ; 1809-1872) * Rudolff, Christoff * Povijesna znanost. Pomoæne povijesne znanosti * Hrvatska povijest 1. Kostrenèiæ, Marko (pravnik i povjesnièar ; 1884-1976) 2. Novak, Grga 3. Herkov, Zlatko (pravnik i povjesnièar ; 1904-1994) 001 / Ljudevit Gaj 002 / Problemi redigiranja Rjeènika domaæeg srednjovjekovnog latiniteta 003 / Presjek kroz imovno stanje i obaveze stanovnika Osijeka (poèetkom 2. polovice 18. stoljeæa) 004 / Prinosi za upoznavanje naših starih mjera za dužinu i površinu ... 016 / Vervlenie v XVII i XVIII vekah

15. The Radical Symbol The Radical Symbol. Before symbols, the words "roots" or "side" were commonly used for the square root of a number. The symbol was introduced by christoff rudolff in 1525 in his book Die Coss http://www.und.nodak.edu/instruct/lgeller/radical.html

The Radical Symbol Before symbols, the words "roots" or "side" were commonly used for the square root of a number. Arab writers thought of a square number as growing out of a root, so Arabs often used the word radix , "extracting," or pulling out, the root. Latin writers thought of it as "finding" the latus, or side of a square. Late medieval Latin writers turned radix into a single symbol R x . This was used for more than one hundred years. The French writer Nicolas Chuquet (1484) sometimes used R x for R x , R x and R x for cube and fourth roots, respectively. The symbol was introduced by Christoff Rudolff in 1525 in his book Die Coss . It is believed this symbol was used because it resembled a small r radix ) at the time. The cube and fourth roots were as shown below: Cube Root Fourth Root Rudolff's symbol was not immediately used. The letter l (latus, "side") was often used. For example the square root of 4 was l 4 and the third root of 5 was lc 5. By the seventeenth century, the square root symbol was being used regularly even though there were many ways the indices were written for higher roots.

16. CHRISTOFF RUDOLFF Translate this page christoff rudolff. Die Nachrichten über das Leben des christoff Rudoll (Ludolff)sind sehr spärlich. rudolff wurde vor 1500 in Jauer (Schlesien) geboren. http://page.mi.fu-berlin.de/~froetsch/manosem/Helle/Rudolff.html

CHRISTOFF RUDOLFF eine Coss ein Rechenbuch namens Kunstliche rechnung (1526), von dem im 16. Jahrhundert nicht weniger als 11 Auflagen gedruckt wurden; (Augsburg 1530). Behend vnd Hubsch Rechnung durch die kunstreichen regeln Algebre so gemeincklich die Coss genennt werden Regulae Cosae vel Algebrae Wurzelzeichen . Er forderte seine Leser auf : "Lernt die zalen der coss aussprechen vnnd durch ire charakter erkennen vnd schreiben." Literatur F. Cajori: A History of Mathematical Notations, vol. 1, La Salle (Illinois) 1928. D. E. Smith: History of Mathematics, vol. 1-2, New York 1958 (1951, 1953. Republication).

17. Zeittafel Translate this page Die ersten Autoren, von denen die Verwendung des modernen Wurzelzeichens überliefertist, waren christoff rudolff und der allseits bekannte Adam Riese (1492 http://page.mi.fu-berlin.de/~froetsch/manosem/Helle/Wurzel.html

Johannes Widmann Das Symbol setzt sich aus zwei Zeichen zusammen. Als erstes ist links der Kleinbuchstabe r zu erkennen. Dem r l unserer heutigen Schreibschrift hat. Es handelt sich jedoch hierbei nicht um ein l Christoff Rudolff und der allseits bekannte Adam Riese (1492-1559). Bei Rudolff taucht das Wurzelzeichen (freilich noch mit einigen Unterschieden zur heutigen Form) erstmals im Druck auf, und zwar im Buch Behend vnd Hubsch Rechnung durch die kunstreichen regeln Algebre so gemeincklich die Coss genennt (1525). Seine heutige Form verdankt das Wurzelzeichen dem Theologen und Mathematiker Michael Stifel , der es in seinem Buch Arithmetica integra (1544) verwendete. Im Zeitraum von 1550 bis 1610 fand das Wurzelzeichen in Europa allgemein Verbreitung. nichts weiter als ein stilisiertes r entstanden sein soll. Zeittafel Literatur F. Cajori: A History of Mathematical Notations, vol. 1, La Salle (Illinois) 1928. D. E. Smith: History of Mathematics, vol. 2, New York 1958 (1951, 1953. Republication).

18. Origin Of The Radical Sign was introduced by the German mathematician christoff rudolff in 1525 in his book "Die Coss". It is generally believed http://chuwm.tripod.com/surd

var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" The Square Root Sign The square root sign ( ) was introduced by the German mathematician Christoff Rudolff in 1525 in his book "Die Coss". It is generally believed that the sign was used because of the letter "r" (which stands for "root"): Back

19. R Index Jakob (132*) Rosenhain, Johann (146) Roth, Klaus (706*) Roth, Leonard (97*) Routh,Edward (152) Rudio, Ferdinand (268*) rudolff, christoff (172) Ruffini, Paolo http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/R.htm

Names beginning with R The number of words in the biography is given in brackets. A * indicates that there is a portrait. Rademacher , Hans (95*) Rado, Richard Radon , Johann (157*) Rahn , Johann (79) Rajagopal , Cadambathur (258*) Ramanujan , Srinivasa (2798*) Ramsden , Jesse (112*) Ramsey , Frank (71*) Rankine , William (118*) Raphson , Joseph (765) Rasiowa , Helena (876*) Rayleigh , Lord John (190*) Razmadze , Andrei (64) Recorde , Robert (282*) Rees , Mina (1102*) Regiomontanus Reichenbach , Hans (125) Reidemeister , Kurt (472*) Reiner , Irving (430) Remez , Evgeny (196*) Rey Pastor , Julio (53) Reye , Theodor (309*) Reymond , Paul du Bois- (137*) Reynaud Reyneau , Charles (137) Reynolds , Osborne (99*) Rham , Georges de (741*) Rheticus , Georg (1559) Riccati , Jacopo (202*) Riccati, Vincenzo Ricci, Matteo Ricci, Michelangelo Ricci-Curbastro, Georgorio ... Richardson , Lewis (273*) Richer , Jean (357) Richmond , Herbert (725*) Riemann , G F Bernhard (2707*) Ries , Adam (380*) Riesz, Frigyes Riesz, Marcel Ringrose , John (544*) Roberts , Samuel (389*) Roberval , Gilles de (349) Robins , Benjamin (375) Robinson, Abraham

20. Mathematicians In Richard S. Westfall's Archive Ricci, Michelangelo; Richer, Jean; Ries, Adam; Roberval, Gilles; Rolle,Michel; Roomen, Adriaan van; rudolff, christoff; Saccheri, Giovanni; http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Wstfllls.htm

Mathematicians in Richard S. Westfall's archive Richard Westfall's archive contains concise biographical details of more than 640 members of the Scientific Community of the 16th and 17th Centuries. The mathematicians who have biographies in our archive are listed below. You can search the whole archive in several ways or can click on a name below. Angeli, Stephano Arbuthnot, John Arnauld, Antoine Bachet, Claude ... Search Suggestions JOC/EFR November 1998

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