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. Sistemidinumerazionesol morse. 1718. Agnesi Maria G. cinese. 1499. rudolff christoff.TARTAGLIA. geroglifico. egizio. 256. Nessuno. babilonese. 1999. Nessuno. maya.352. http://www.matematico.it/GIOCHI/GiochiMatematicamente/sistemidinumerazionesol.ht

giochi gara 2001-2002 sistemi di numerazione - soluzione di G.Valentini matematici base 10 Borel Felix E. Drach Jules J. Enriques Federigo Epstein Paul Fano Gino Galerkin Boris G. Gjunter Nikolaj M. Heegaard Poul Steinitz Ernst Yule George U. Zermelo Ernst F.F. base 2 Argand Jean R. Fourier Jean B. Français François J. Servois François J. Wallace William MDCCCLXII romano Bjerknes Vilhelm F.K. Campbell John E. Gentry Ruth Hilbert David Kneser Adolf Merrill Winifred E. Moore Eliakim H. Macaulay Francis S. Richard Jules A. Stackel Paul G. Study Eduard morse Agnesi Maria G. cinese Rudolff Christoff TARTAGLIA geroglifico egizio Nessuno babilonese Nessuno maya nessuno Greco antico nessuno azteco nessuno brahmi nessuno

3. Rudolff [Rudolf], Christoff Biography of christoff rudolff (14991545) christoff rudolff. Born 1499 in Jauer, Silesia (now Jawor, Poland) 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.

4. CHRISTOFF RUDOLFF References for the biography of christoff rudolff References for christoff rudolff. Biography in Dictionary of Scientific Biography (New York 19701990). http://www.inf.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).

5. Rudolfinische Hausordnung Translate this page Rotunde - Rudolfinische Hausordnung (25/25). rudolff, christoff, Rotunde - RudolfinischeHausordnung. Rudolfinische Hausordnung. Rudolfinische Hausordnung, am 18. http://www.aeiou.at/aeiou.encyclop.r/r937716.htm

A B C D ... Rudolfinische Hausordnung - Ruprecht, Heiliger Rudolfinische Hausordnung Rudolfinische Hausordnung, am 18. 11. 1364 getroffene Festlegung des gemeinsamen Besitzes der ungeteilten habsburgischen zwischen Rudolf IV., Albrecht III. und Leopold III. Hinweise zum Lexikon Suche nach hierher verweisenden Seiten

6. Adam Riese (1492-1559) And Christoff Rudolff's (1499-1545) Adam Riese (14921559) and christoff rudolff's (1499-1545) http://www.soi.city.ac.uk/~msch/talks/boole/tsld014.htm

Adam Riese (1492-1559) and Christoff Rudolff's (1499-1545) They were also used in the books ``Die Coss'', written in 1524 by the celebrated Rechenmeister Adam Riese (1492-1559), which promoted Hindu-Arabic numerals and calculation by pen instead of counting with an Abacus, and in Christoff Rudolff's (1499-1545) ``Coss'', published in 1525, which also introduced the sqrt-sign first. Previous slide Next slide Back to first slide View graphic version

7. Bayerische Staatsbibliothek - Förderverein rudolff, christoff Künstliche rechnung mit der Ziffer und mit den zal pfennigen sampt der Wellischen Practica und http://www.bsb-muenchen.de/foerder/p484.htm

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

8. Biography-center - Letter R Rudolf, Leopold. rudolff, christoff. Rudolfinische Hausordnung http://www.biography-center.com/r.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 R 483 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Renyi.html R. M., Williams www.abc.net.au/btn/australians/rmwilliams.htm Rabbitt, Eddie elvispelvis.com/eddierabbitt.htm Rabi, Isidor www.pbs.org/wgbh/amex/bomb/peopleevents/pandeAMEX80.html Rabi, Isidor Isaac www.nobel.se/physics/laureates/1944/rabi-bio.html Rabiah ibn Kab, www.usc.edu/dept/MSA/history/biographies/sahaabah/bio.RABIAH_IBN_KAB.html Rabin, Yitzhak www.nobel.se/peace/laureates/1994/rabin-bio.html Rabinow, Jacob web.mit.edu/invent/www/inventorsR-Z/rabinow.html Rachmaninoff, Sergei www.island-of-freedom.com/RACH.HTM Rackham, Arthur www.bpib.com/illustrat/rackham.htm#rackhamtop www-history.mcs.st-and.ac.uk/~history/Mathematicians/Rado.html Rademacher, Hans

9. 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/history/References/Rudolff.html

10. Rudolff, Christoff Translate this page rudolff, christoff. rudolff, christoff, * 1500 (?) Jauer (Jawor, PL),† 1545 Wien, Mathematiker. Schüler von Grammateus in Wien. 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

11. Rudolff [Rudolf], Christoff rudolff Rudolf, christoff. Note the creators of the Galileo Projectand this catalogue cannot answer email on geneological questions. http://es.rice.edu/ES/humsoc/Galileo/Catalog/FilesOLD/rudolff.html

Rudolff [Rudolf], Christoff Note: the creators of the Galileo Project and this catalogue cannot answer email on geneological 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. 10. Scientific Societies

12. R Index Rudio, Ferdinand (268*). rudolff, christoff (172). Ruffini, Paolo (2196*) http://www-groups.dcs.st-and.ac.uk/~history/Indexes/R.html

Names beginning with R The number of words in the biography is given in brackets. A * indicates that there is a portrait. Rademacher , Hans (531*) Rado, Richard Radon , Johann (157*) Rahn , Johann (79) Rajagopal , Cadambathur (258*) Ramanujam , Chidambaram (1636*) Ramanujan , Srinivasa (2798*) Ramsden , Jesse (112*) Ramsey , Frank (1319*) Ramus , Peter (1262*) Rankin , Robert (1546*) Rankine , William (118*) Raphson , Joseph (765) Rasiowa , Helena (876*) Rayleigh , Lord (J Strutt) (190*) Razmadze , Andrei (373) Recorde , Robert (2383*) Rees , Mina (1102*) Regiomontanus Johann (341*) Reichenbach , Hans (125*) Reidemeister , Kurt (472*) Reiner , Irving (436) Remak , Robert (1039*) Remez , Evgeny (196*) Rey Pastor , Julio (404*) Reye , Theodor (309*) Reymond , Paul du Bois- (137*) Reynaud Reyneau , Charles (351) Reynolds , Osborne (926*) Rham , Georges de (741*) Rheticus , Georg Joachim (1559) Riccati, Jacopo Riccati, Vincenzo Ricci, Matteo Ricci, Michelangelo ... Richardson , Lewis (273*) Richer , Jean (357) Richmond , Herbert (725*) Riemann , G F Bernhard (2707*) Ries , Adam (380*) Riesz, Frigyes

13. Adam Riese (1492-1559) And Christoff Rudolff's (1499-1545) First Previous Next Last Index Home Text. Slide 14 of 42. http://www.soi.city.ac.uk/~msch/talks/boole/sld014.htm

First Previous Next Last ... Text Slide 14 of 42

14. 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 Die Buchpaten 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

15. Rechnen1.html Translate this page Es hat christoff rudolff vom Jawer löblicher Gedechtnis anno 1524 die wunderbarlicheund ganz Philosophische Kunst des rechnens / genennet die Coss / in http://www.mathematik.uni-bielefeld.de/~sieben/Rechnen/Rechnen1.html

Ein bisschen Geschichte Anleitungen zum Rechnen hat man auf Keilschrifttafeln allerdings nicht gefunden. Leonhard Euler in einem kurzen Lebenslauf, den er seinem Sohn Johann Albrecht 1767 diktierte. Dort heisst es: Mit Blick auf den heutigen Rechenunterricht - Slogan: `Von Kindern lernen!' Leonhard Euler als Kind Michael Stifel , der 1553 die Coss Christoph Rudolphs mit eigenen Anmerkungen neu herausgab, sprach die Hoffnung aus, dass sein Leser Stifel ist bestrebt, das Rechnen zu vereinfachen und die Zahl der Regeln zu vermindern: denn es ist mein fleiss in sollichen sach / das ich (wa ich kan) aus vielfeltigkeit mache ein einfeltigkeit. Also hab ich auss vielen Regeln der Coss ein einige Regel gemacht; wer da will viel vnd schwere ding leychtlich lernen und behalten / der hab wol acht auff solliche vereinigung. In seiner Vorrede zu dem Buch sagt Stifel: heymlich vnd thewr ist die Coss gehalten worden / bei denen die sie gekundt haben / ehe Christopf Rudolff sie vns hat mitgeteylet / das ich vielleicht auch nymmermehr erfahren hette, was die Coss were. Derohalben hab ich mich vnderwunden Chr. Rudolffs arbeit zu mehren / seyn Buch von Wort zu Wort abzuschreiben/ und jedem capitel meynen Anhang zu setzen.

16. Algebra In The Renaissance, Part 1 of Pisa, Luca Pacioli, the Summa de Arithmetica, Geometrica, Propotioni et Proportionalita, Nicolas Chuquet, the Triparty, christoff rudolff, Michael Stifel http://public.csusm.edu/public/DJBarskyWebs/330CollageOct15.html

Algebra in the Renaissance, Part 1 Student lecturer Jennifer Hineline started today's discussion with an overview of the social climate of the Renaissance era, specifically the economic situation. Instead of traveling to buy and returning home to sell, merchants would hire others to do the traveling and buying. This complicated the accounting process, bringing about a need for mathematicians as accountants. Ms. Hineline also made a connection between the ease with which Arabic numerals can be altered and the practice of writing out numbers in other ways, which is still in practice today in the writing of checks. After a brief discussion of some of the symbolic notation used by some Italian algebraists, Ms. Hineline explained Paolo Gerardi's algorithm for adding algebraic fractions. This was very similar to what we teach in beginning algebra, except that instead of necessarily finding the lowest common denominator, Gerardi would simply use the product of the denominators of all the addends. Ms. Hineline then discussed Maestro Dardi and his method of solving cubic equations. Unfortunately, Dardi's method only works when certain relationships exist between the coefficients. Ms. Hineline proceeded to introduce a series of mathematicians from France, Germany, England and Portugal, paying special attention along the way to Nicolas Chuquet from France. Chuquet theorized that given two ratios, a/b and c/d, the ratio (a+c)/(b+d) would fall between the two original ratios. Ms. Hineline demonstrated Chuquet's method of estimating square roots using his ratio theory. Although he never used the word limit, Chuquet was using a variation of the squeeze theorem and a limiting process to find square roots. Chuquet realized that square roots that are not integers are irrational, and he acknowledged that his method would never allow him to find a square root exactly. But by taking this method far enough, we can come arbitrarily close to the actual root, and we can estimate a root to any desired degree of accuracy.

17. Earliest Uses Of Symbols For Fractions And Decimals In 1530, christoff rudolff (1499?1545?) used a vertical bar exactly as we use adecimal point today in setting up a compound interest table in the Exempel B http://mail.mcjh.kl.edu.tw/~chenkwn/mathword/fractions.html

Earliest Uses of Symbols for Fractions and Decimals Last revision: June 19, 1999 Earliest notations for fractions. Information on Babylonian, Egyptian, and Greek fractions will be added to this page soon. Ordinary fractions without the horizontal bar. According to Smith (vol. 2, page 215), it is probable that our method of writing common fractions is due essentially to the Hindus, although they did not use the bar. Brahmagupta (c. 628) and Bhaskara (c. 1150) wrote fractions as we do today but without the bar. The horizontal fraction bar was introduced by the Arabs. "The Arabs at first copied the Hindu notation, but later improved on it by inserting a horizontal bar between the two numbers" (Burton). Several sources attribute the horizontal fraction bar to al-Hassar around 1200. When Rabbi ben Ezra (c. 1140) adopted the Moorish forms he generally omitted the bar. Fibonacci (c.1175-1250) was the first European mathematician to use the fraction bar as it is used today. He followed the Arab practice of placing the fraction to the left of the integer (Cajori vol. 1, page 311). The bar is generally found in Latin manuscripts of the late Middle Ages, but when printing was introduced it was frequently omitted, doubtless owing to typographical difficulties. This inference is confirmed by such books as Rudolff's

18. Earliest Uses Of Symbols For Fractions In 1530, christoff rudolff (1499?1545?) used a vertical bar exactly as we usea decimal point today in setting up a compound interest table in the Exempel http://members.aol.com/jeff570/fractions.html

Earliest Uses of Symbols for Fractions Last revision: Jan. 15, 2003 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.

19. Earliest Uses Of Symbols For Variables christoff rudolff used the letters a, c, and d to represent numbers, although notin algebraic equations, in Behend vnnd Hubsch Rechnung (1525) (Cajori vol. 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].

20. Untitled Document Translate this page Jacob Köbel 1514. Ain New Gordnet Rechen Biechlin 1514. christoff rudolff 1525.Coss 1525. christoff rudolff 1525, Die Regel de Tri. A regra de três. Coss 1525. http://www.prandiano.com.br/html/m_arq2.htm

AUTOR Ahmed Ibn 860 d.C. para o latim em 1231 d.C. por Robertus Anglicus Leonardo de Pisa (Fibonacci) IL Liber Abbaci di Leonardo Pisano Georg Joachin Rheticus Canon Doctrinae Triangulorum Francisco Maurolyco Menelai Sphaericorum Libri Tres Edmund Gunter Description and use of The Sector Entende-se a palavra latina sinus como fundo de uma palavra em italiano arcaico podia ser feita nas seguintes formas: AUTOR Hoje Ontem Leonardo de Pisa Liber Abbaci Nicolau Oresme Algorithmus Proportionum Jacob Ain New Gordnet Rechen Biechlin Christoff Rudolff Coss (Gerdanus) Algorithmus Demonstratus Nicolo Tartaglia General Tratado De Numeri Juan Perez de Moya Arithmetica Practica Ciacchi de Florence Regole Generali d'Abbaco Tobias Beutel Geometriche Gallerie Manuel Valdes Gazeta de Mexico Augustus De Morgan The Calculus of Functions FRACTION FRACTUS (quebrado)

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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