1. Rudolff Christoff Rudolff. Born Version for printing. Christoff Rudolff studied algebraat the University of Vienna, between 1517 and 1521. He http://www.gap-system.org/~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 Version for printing 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. Rudolff Christoff Rudolff. Born 1499 in Christoff Rudolff studied algebra at theUniversity of Vienna, between 1517 and 1521. He remained in http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Rdlff.htm

3. Rudolff Biography of christoff rudolff (14991545) christoff rudolff studied algebraat the University of Vienna, between 1517 and 1521. 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 Version for printing 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.

4. References For Rudolff References for the biography of christoff rudolff. W Kaunzner, Über christoffrudolff und seine Coss , Ein Beitrag zur Geschichte der Rechenkunst zu http://www-groups.dcs.st-and.ac.uk/~history/References/Rudolff.html

References for Christoff Rudolff Version for printing 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

5. Rottmeyer, Franz Robert - Rudolff, Christoff Rot-Weiß-Rot Rubatscher, Maria Veronika Rübelt, Lothar Rübentaler 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

6. Rudolff, Christoff Translate this page Rottmeyer, Franz Robert - rudolff, christoff (25/25) rudolff, christoff, *1500 (?) Jauer (Jawor, Polen), † 1545 Wien, Mathematiker. 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

7. 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>

8. Hrvatska Akademija Znanosti I Umjetnosti. Knjižnica 007 / christoff rudolff und das Problem seiner Masse 008 / Metrologie du selet histoire comparée en Méditerranée 009 / Das ursprüngliche System der 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

9. Katalog Rothe, Hans Rovanjska Rubbia, Carlo Rude (2) Rudolf, Davorin (pravnik ;1934) (3) rudolff, christoff Rukavina, Daniel (lijecnik ; 1937-) http://161.53.55.45/HAZU-POV/per/predmet/indeks82.htm

Predmet - Èasopisi Rab Racz, Zoltan (agronom ; 1930-) Raèki, Franjo Raèki, Franjo (povjesnièar ; 1828-1894) ... Ružièka, Lavoslav (kemièar ; 1887-1976)

10. Mathematical Symbols His pupil christoff rudolff, the writer of the first text book on algebra in theGerman language (printed in1525) employs these symbols. http://www.roma.unisa.edu.au/07305/symbols.htm

The History of Mathematical Symbols By Douglas Weaver Mathematics Coordinator, Taperoo High School with the assistance of Anthony D. Smith Computing Studies teacher, Taperoo High School. Introduction On the topic of mathematical symbols..... "Every meaningful mathematical statement can also be expressed in plain language. Many plain-language statements of mathematical expressions would fill several pages, while to express them in mathematical notation might take as little as one line. One of the ways to achieve this remarkable compression is to use symbols to stand for statements, instructions and so on." Lancelot Hogben Index The factorial symbol n! The symbols for similar and congruent The symbols for angle and right angle The symbol pi ... APPENDIX - Personalities select here to return to the HoM home page The factorial symbol n! The symbol n!, called factorial n, was introduced in 1808 by Christian Kramp of Strassbourg, who chose it so as to circumvent printing difficulties incurred by the previously used symbol thus illustrated on the right. (Eves p132) The symbol n! for "factorial n", now universally used in algebra, is due to Christian Kramp (1760-1826) of Strassburg, who used it in 1808. (Cajori p341)

11. List Of Poles: Information From Answers.com christoff rudolff. Stanislaw Saks. Friedrich Schottky. Waclaw Sierpinski.Yulian Sokhotsky. (unconfirmed); Mikhail Subbotin (of Russian origin). http://www.answers.com/topic/list-of-poles

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping List of Poles Wikipedia List of Poles This is a partial list of famous Polish Polish-speaking/writing people, and people born in Poland Science Astronomy Franciszek Arminski Nicolas Copernicus Tadeusz Banachiewicz Wladyslaw Dziewulski ... Johannes Hevelius (of Czech origin). Marcin Kubiak Konrad Rudnicki Andrzej Udalski Wieslaw Wisniewski Biology Joseph Babinski , physician Edmund Biernacki , physician Czeslaw Biezanko , famous entomologist Adam Gruca , surgeion Stanislaw Burzynski , famous physician Tytus Chalubinski , physician Napoleon Cybulski , famous neurophysiologist Maria Antonina Czaplicka , anthropologist Wiktor Dega , revolutionary surgeon August Dehnel , biologist Jozef Dietl , physician Emil Godlewski , embryologist Ludwik Hirszfeld , microbiologist Stefan Kopec , biologist Rudolf Wiegl , biologist Jan Czekanowski , anthropologist Marek Kotanski , pschychologist Zbigniew Kabata , biologist Jan Kubary , anthropologist Hilary Koprowski , famous biologist Andrzej Wiktor Schally , endocrynologist Boleslaw Skarzynski , biologist Wojciech Jastrzebowski , biologist Konstanty Jelski , ornithologist Jerzy Konorski , microbiologist Tadeusz Krwawicz , medical pioneer Marie Elizabeth Zakrzewska , physician Adam Prazmowski , microbiologist , anthropologist Zbigniew Religa , cardiologist Jozef Rostafinski , biologist Bronislaw Malinowski , greatest anthropologist of 20th century Chemistry J³zef Boguski Jan Czochralski Nobel Prize (twice).

12. 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: 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.

13. Earliest Uses Of Symbols For Variables christoff rudolff used the letters a, c, and d to represent numbers, althoughnot in 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].

14. ¥³.The Sixteenth-Century Mathematics Of Italy: Commercial Mathematics His disciple, christoff rudolff used the radical symbol(v) including (+), (),in his bool about algebra in 1525. He used simple the radical symbol (v) as http://seoul-gchs.seoul.kr/~contest/tq/mathematics/temh2400.htm

HOME Back Graphic Version ¥³.The Sixteenth-Century Mathematics of Italy : Commercial Mathematics ¢º Characteristic of The 16th Century Mathematics. ¢º Arrangement of The Symbols ¢ºCubic and Quartic Equations ¡ß Characteristic of The Sixteenth-Century Mathematics ... In summarzing the mathematical achievements of the sixteenth century, We can say that symbolic algebra was well started, computation with the Hindu-Ariabic numerals became standardized, decimal fractions were developed, the cubic and quartic equations were solved and the theory of equations generally advanced, negative numbers were becoming accepted trigonometry was perfected and systematized, and some excellent tables were computed. The stage was set for the remarkable strides of the next century. ¡ß Arrangement of The Symbols Renaissant algebra started with necessity for commerce and arrangement of algebraic symbols. ¡Ý Plus(+) and Minus(-) : These symbols appeared in a book about arithmetic written by John Widmann - Called father of arithmetic - for the first time in 1489. At first, these symbols expressed 'surplus', and 'insufficiency' but later it meant 'addition'and 'subtraction'

15. 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

16. References For Rudolff References for christoff rudolff. Version for printing Biography in Dictionaryof Scientific Biography (New York 19701990). Books http://www-groups.dcs.st-andrews.ac.uk/history/References/Rudolff.html

References for Christoff Rudolff Version for printing 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

17. Math Radical Pin Handcrafted Pewter Pin CC368 size 1 X 1/2 . Math radical pin. The radical symbolfirst appeared in 1525 in Die Coss by christoff rudolff (14991545). http://www.lapelpinplanet.com/science/science_enlarged_pics/radical_large.htm

Math Radical Handcrafted Pewter Pin CC368 size: 1" X 1/2" The radical symbol first appeared in 1525 in Die Coss by Christoff Rudolff (1499-1545).

18. Pythagoras' Constant : $\sqrt{2}$ The history of the famous sign Ö goes back up to 1525 in a treatise named Cosswhere the German mathematician christoff rudolff (14991545) used a similar http://numbers.computation.free.fr/Constants/Sqrt2/sqrt2.html

Pythagoras' Constant : (Click here for a Postscript version of this page.) There are certainly people who regard as something perfectly obvious but jib at . This is because they think they can visualise the former as something in physical space but not the latter. Actually is a much simpler concept. Edward Charles Titchmarsh Introduction The constant 2 is famous because it's probably one of the first irrational numbers discovered. According to the Greek philosopher Aristotle (384-322 BC), it was the Pythagoreans around 430 BC who first demonstrated the irrationality of the diagonal of the unit square and this discover was terrible for them because all their system was based on integers and fractions of integers. Later, about 2300 years ago, in Book X of the impressive Elements, Euclid (325-265 BC) showed the irrationality of every nonsquare integer (consult [ ] for an introduction to early Greek Mathematics). This number was also studied by the ancient Babylonians. The history of the famous sign goes back up to 1525 in a treatise named Coss where the German mathematician Christoff Rudolff (1499-1545) used a similar sign to represent square roots.

19. The Galileo Project rudolff Rudolf, christoff. 1. Dates Born fl Died Dateinfo Dates CertainLifespan; 2. Father Occupation Unknown No information on financial http://galileo.rice.edu/Catalog/NewFiles/rudolff.html

Rudolff [Rudolf], Christoff 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

20. 2 Algebraic Notation of counting with an Abacus, and in christoff rudolff s (14991545) ``Coss ,published in 1525, which also first introduced the $ \sqrt{}$ -sign. http://www.hf.uio.no/filosofi/njpl/vol2no1/history/node2.html

Next: 3 Logic and Computation Up: A Brief History of Previous: 1 Introduction 2 Algebraic Notation Muhammad ibn Musa al-Khwarizmi (780?-847?), who worked at Baghdad's ``House of Wisdom'', is often credited with being the father of algebra. His book ``Al-jabr wa'l muqabalah'', which can be translated as ``restauration and reduction'', gives a straight-forward and elementary exposition of the solution of equations. A typical problem, taken from chapter V, is the division of ten into two parts in such a way that ``the sum of the products obtained by multiplying each part by itself is equal to fifty eight''. The solution, three and seven, is constructed geometrically in quite an elegant fashion. Besides his own methods, al-Khwarizmi uses procedures of Greek origin such as proposition 4 of book II in Euclid's Elements: If a straight line is cut at random, the square on the whole is equal to the squares on the segments and twice the rectangles contained by the segments. Figure 1: Geometric solution of equations. Take a look at Figure . Euclid's theorem states that the sum of the shaded squares and the two remaining rectangles is equal to the whole square. In the case of al-Khwarizmi's problem, the whole square has 100 units since the straight line has ten units. The two shaded squares on the segments have fifty-eight units and so al-Khwarizmi concludes that each rectangle amounts to twenty-one units. To complete the solution of the problem, we quote from Rosen's translation of al-Khwarizmi's Algebra:

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