81. Mathematicians William Buckley (dc 1550). christoff rudolff (c. 1500c. 1545) *SB *mt*W. Niccolò Fontana of Brescia (Tartaglia) (c. 1500-1557) *MT *W. http://www.chill.org/csss/mathcsss/mathematicians.html

List of Mathematicians printed from: http://aleph0.clarku.edu:80/~djoyce/mathhist/mathhist.html 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 Hippias of Elis (fl. c. 425) *SB *mt Theodorus of Cyrene (c. 425) Socrates (469-399) Philolaus of Croton (d. c. 390) *SB Democritus of Abdera (c. 460-370) *SB *mt 400 B.C.E. Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?) Archytas of Tarentum (of Taras) (c. 428-c. 347) *SB *mt Plato (427-347) *SB *MT Theaetetus of Athens (c. 415-c. 369) *mt Leodamas of Thasos (fl. c. 380) *SB

82. New Page 4 Heinrich Schreiber. A student of Schreiber's, christoff rudolff madeextensive use of these symbols in his acclaimed work Coss. In this http://stuweb1.gulfcoast.edu/bookmathematica/Trial page1.1.htm

§1.1 Roots of the Hindu-Arabic Numbers Introduction The ten symbols 9 which are used today by nearly all peoples represents, to quote Karl Menninger from his excellent book Number Words and Number Symbols , "the world-wide victory of an idea." Few things in our world are universally accepted and continuously ongoing, but the surviving concept that effectively rendered all other numbering systems obsolete is the one handed down to us centuries ago from the Hindus and Arabs. The Hindu-Arabic numbering system is named for the Hindus, who appear to have invented it, and the Arabs, who transmitted it to the West. Although the history of India is beyond our scope, an appreciation for some of its highlights is in order so that we may understand how late - as compared to the Egyptians, Greeks, and Babylonians - it was when India finally stepped up to the proverbial plate and hit a mathematical homerun with her contribution to the world. In looking back, her gift of ten simple symbols combined with a place-valued numbering system may be argued as being the most important of all offerings to mathematics and mankind. The Hindus Of no small consequence is the fact that the northwest part of India (Gandhara) was part of the Persian Empire from the 6 th century B.C. on. In his quest to conquer Persia, Alexander the Great invaded this region around 325 B.C. It was at this time that Greek culture, including mathematics and astronomy, took refuge in India. What is known as Gandhara art is a direct result of the mixture of East and West. Clearly the most important result of this incursion was that now a route for the exchange of ideas and culture existed between India and her distant neighbors to the west.

83. Genealogie - Wandel In Den Vornamen / Männer Translate this page Cheb, Christian, Christianus, Christen. Christopher, christoffer, Christofer, christoff,Christoph. Claude, Rolf, Rudolph, rudolff, Rudolf, Rolfs. Rotgartt, Salomon, http://www.peter-doerling.de/Geneal/VornamenM.htm

Genealogie - Wandel in den Vornamen / Männer (Men) Link zu Vornamen / Frauen (Women) Vorname Variationen Abraham Adam = Erdmann Adolf Adolph Adrian Ahlert Ehlert Albert Albinus Albrecht Alexander Alfred Amandus Andreas / Drews Anderß, Andreaß, Andres, Andreß, Endreß Anselmus Anton Anthon, Antony Arndt Arend, Ahrend, Arendt, Arnt Arnold Arnoldus Arp Arps, Arfft Arries Asmus Aßmus, Aßmuß August Augustin, Augustus Axel Balthasar Baltasar, Balster, Baltzar, Baltzer Bartel Bartholomeus, Bartolomeuss, Bartelmus, Barteld, Barteldt, Bartelt, Bartheldt, Barthel Bartold Bartholdus, Bartoldus, Bartholdt, Barthold, Bartoltt Bartram Battram Basche Basilius Bendix Benedictus, Benedix, Benecke, Beneke, Bencke Benjamin Bernd Behrend, Berendt, Berend, Berent, Bernt Bernhard Bernhart Bert Berthold, Berteldt, Bertelt Bintin Blasius Bleß Borchard Burchardus, Burchard, Borchart Brun Burwin ? Buß Caesar Carl Carol Casimir Casymir, Caßmers Caspar Casparus, Casper, Caßpar Charles Cheb Christian Christianus, Christen Christopher Christoffer, Christofer, Christoff, Christoph Claude Claus / Klaus Clauwes, Clawess, Clawes, Claws, Clawß, Claves, Claues, Claes, Claars, Claaß, Claas, Class, Claß, Clas, Clauß

84. 2000 ”N‚Ì Column ? William Oughtred (), 1574.3.51660.6.30 Clavis Mathematicaev ? christoff rudolff, 14991545. , ? Thomas http://www.nn.iij4u.or.jp/~hsat/column/col00.html

2000 ”N‚Ì column ‚ªŽ¦‚µ‚½•û–@‚ɂǂꂾ‚¯‚̐V‚µ‚¢‚à‚Ì‚ð•t‚¯‰Á‚¦‚邱‚Æ‚ªo—ˆ‚½‚Ì‚¾‚낤‚©, ‚ÆŠ´‚¶‚Ä‚¢‚é‚Ì‚ÍŽ„‚¾‚¯‚¾‚낤‚©B Îˆäˆê•½, Œc‰ž‹`m‘åŠw—HŠw•” ŽO‘Ì–â‘襐§ŒÀŽO‘Ì–â‘è “ÁW “V‘Ì‚Ì“®‚«‚ð’Ç‚Á‚½”ŠwŽÒ’B ”ŠwƒZƒ~ƒi[ (7), 1999. ¬à‰Æ‚ɂȂ邽‚߂ɐ”Šw‚ðŽ~‚ß‚½ˆ½‚éŠw¶‚ɂ‚¢‚Ä David Hilbert (18621943) ‚ªŒ¾‚Á‚½Œ¾—t —L–¼‚È de Moivre‚ÌŒöŽ®‚Í de Moivre (16671754, UK) ‚Ì’˜ì u‹‰”‚Æ‹Ï‚ÉŠÖ‚·‚鐔ŠwŽG˜^v (London, 1730) ‚̈ê•Å–ڂɏo‚Ä‚¢‚é‚Æ‚¢‚¤B —L–¼‚È“ñ€’藝‚Ì”­Œ©‚Í Sir Isaac Newton (16421727) ‚Å, 1665 ”N ‚Ì‚±‚Æ‚Å‚ ‚é‚Æ‚¢‚¤B •¶Œ£“I‚É‚Í 1676 ”N 6 ŒŽ 13 “ú•t‚̎莆‚Ì’†‚ɏ‰‚ß‚ÄŒ©‚ç‚ê‚é‚Æ‚¢‚¤B ƒJƒWƒ‡ƒŠ u‰“™”ŠwŽjv (‹¤—§o”Å, p. 340 ŽQÆ) ‚£³m, ”ŠwŽÒ¥”ŠwŽj‰Æ dx ‚Æ dy ‚̉ðÍŠw -ƒIƒCƒ‰[‚ÉŠw‚Ô- II. ƒIƒCƒ‰[‚̐¢ŠE (‚»‚Ì2) ”ŠwƒZƒ~ƒi[ (8), 1999 Ž©‘R‘ΐ”‚Ì’ê e ‚Ì‚±‚Æ‚ð‘o‹Èü‘ΐ”‚ƌĂԂ±‚Æ‚ª‚ ‚é‚Ì‚¾‚»‚¤‚¾B ‚±‚ê‚Í’¼Šp (“™•Ó) ‘o‹Èü xy = 1 ‚Æ x Ž², “ñ’¼ü x = 1, x = t ‚ň͂܂ê‚é•”•ª‚Ì–ÊÏ S ‚ª S = ç ƒJƒWƒ‡ƒŠ ¢‰“™”ŠwŽj£ (‹¤—§o”Å) p.235ŽQÆ‚Ì‚±‚ƁB ŽO•Ó‚Ì’·‚³‚ª‘S‚Đ®”‚Å‚ ‚éŽOŠpŒ`‚É‚¨‚¢‚Ä, ‚»‚ê‚çŽO•Ó‚̘a‚Æ‚»‚̖ʐςƂª“™‚µ‚­‚È‚é‚悤‚ÈŽOŠpŒ`‚Í, ‚»‚ÌŽO•Ó‚Ì’·‚³‚ª, (6, 8, 10), (5, 12, 13), (9, 10, 17), (7, 15, 20), (6, 25, 29) ‚Å‚ ‚é‚à‚Ì‚ÉŒÀ‚éB (‚±‚ê‚ç‚Í‘S‚Ä, ®”•Ó’·‚Ì’¼ŠpŽOŠpŒ` [ƒsƒ ƒ^ƒSƒ‰ƒXŽOŠpŒ`] ‚©‚çƒsƒ ƒ^ƒSƒ‰ƒXŽOŠpŒ`‚ð uˆø‚¢‚½v ‚à‚Ì‚É‚È‚Á‚Ä‚¢‚é) ‚»‚µ‚Ä (®”•Ó’·‚Å‚Í‚È‚­‚Æ‚à) ŽO•Ó‚̘a‚ƖʐςƂª“™‚µ‚¢ŽOŠpŒ`‚É‚¨‚¢‚Ä‚Í, ‚»‚Ì“àÚ‰~‚Ì”¼Œa‚Í2‚É‚È‚éB ‰~‚̃R[ƒc‚̐«Ž¿: x k=1 n (x2 - 2x cos((2k - 1)ƒÎ/(2n)) + 1).

85. Vernon (Bilander) 1747 Translate this page Jacob Steinkönig ?, Henrich Starzman, christoff Cressel, David Scheider, Sheyder.Jacob Leesher, Henrich Huber, Heinrich Huber, Hans rudolff Br, Jacob Steinbrüchel, http://www.palproject.org/pa/1747vern.htm

1747 Vernon (Bilander) [List 112 C] Vernon (Bilander) Captain: Thomas Ricks From: Rotterdam By Way of: Leith, Scotland Arrival: Philadelphia, Aug 1747 Name, Age Place of Origin (Town, Province) Source Remarks (USA, Spelling Variations, Occupation, Relationships, etc.) Andreas Bürger Christofel Br Jacob Steinkönig [?] Henrich Starzman Christoff Cressel David Scheider Sheyder Jacob Leesher Joseph Grünwalt Hans Michael Kuntz Henrich Büttner Hans Michael Brüttner Schwaigern, Baden To Lancaster Co. Samuel Witmer Marx Egli Tobias Wagheman Henrich Grub Abraham Funk Johannes Meingssner Hans Caspar Feerer Johannes Rooghel Jacob Schappy Hans Jacob Schappy Hans Nickel Schmitt Hans Wilhelm Weidner Felix Weiss Hans Rudi Wis Hans Bickell Hans Bleigestaufer Jacob Schnebeli Rudolph Hornecker Rudolph Hornecker, Jr. Ulrich Hornecker Henrich Hecker Peter Bawman Hans Jacob Wallder Johannes Walder Hans Henrich Walder Hans Casper Wallder Hans Michael Eysenman Ludwig Weiter Rudolf Huber Jacob Huber Johann Christian Wampfler Jörg Wampffler Christian Wampfler Johann Ludwig Wampffler Henrich Huber Heinrich Huber Hans Rudolff Br Jacob Steinbrüchel Hans Frick Hans Gorg Schorr Killian Indorff Heinrich Fink Friederich Wirtz Wilhelm Otz Last Modified: 16 May 2002

86. ThinkQuest Library Of Entries European Developments. Nicolas Chuquet of France and christoff Rudolffof Germany both developed systems of exponential notation. http://library.thinkquest.org/C0110248/algebra/history2.htm

Welcome to the ThinkQuest Internet Challenge of Entries The web site you have requested, , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to click here Back to the Previous Page The Site you have Requested ... click here to view this site A ThinkQuest Internet Challenge 2001 Entry Click image for the Site Awards Received Achievement Award Site Desciption 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! Students Teow Lim Raffles Junior College Singapore Vee San Raffles Girls' School (Secondary) Singapore Coaches Poh Kheng Pioneer Junior College Singapore Jee Wah Raffles Girls' School (Sec) Singapore

87. Les Origines Des Notations Mathématiques Translate this page D'où vient le symbole des radicaux ? Ce symbole est dû à l’AllemandChristoff rudolff en 1525, dans son ouvrage die Coss. C http://perso.club-internet.fr/rferreol/langage/notations/notations.htm

88. Thisle Of Glasgow 1730 ChristoffBatter. Stefen Reiner. Johann rudolff Drach Maria Elisabetha Elisabetha, 2. http://www.palproject.org/pa/1730thisle.htm

1730 Thisle of Glasgow [List 11 A, B] Thisle of Glasgow Captain: Colin Dunlop From: Rotterdam, June 1730 By Way of: Dover (19 June 1730) Arrival: Philadelphia, 29 Aug 1730 Seventy-seven Palatines, who with their families, make about two hundred and sixty persons. A study of the individuals and families on this ship, especially those from the region of Ludwigshafen a. Rhein, was made by Fritz Braun in 1730 and published in Schriften zur Wanderungsgeschichte der Pfälzer Vol. 8 (1959) under the title, Auswanderer aus der Umgebung von Ludwigshafen a. Rh. auf dem Schiff "Thistle of Glasgow" 1730. Name, Age Place of Origin (Town, Province) Source Remarks (USA, Spelling Variations, Occupation, Relationships, etc.) Johann Georg Ludwig Haas, 29 Anna Margaretha (Stahler), 27 Maria Barbara, 4 Johann Balthasar, 3 Hassloch, Bayern (Pfalz) Jörch; to Philadelphia, and Lancaster, PA. Bernhardt Sigmundt Sighmond; In Philadelphia 1734-1739 Johann Valentin Griesemer, 42 Anna Margaretha (Andreass) Johann Wilhelm, 17

89. DAS COSS bezeugen alte bücher nit vor wenig jaren von der coss geschriben, in welchen http://www.inf.fu-berlin.de/~froetsch/manosem/Helle/Coss.html

DAS COSS Christoff Rudolff Coss Christoff Rudolff und Michael Stifel , in England der Arzt Robert Recorde Literatur F. Cajori: A History of Mathematical Notations, vol. 1, La Salle (Illinois) 1928. D. E. Smith: History of Mathematics, vol. 1, New York 1958 (1951, 1953. Republication).

90. The Radical Symbol and fourth roots, respectively. The symbol was introduced by ChristoffRudolff in 1525 in his book Die Coss. It is believed this http://www.und.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.

91. Earliest Uses Of Symbols Of Operation And Grouping 2, page 78). The radical symbol first appeared in 1525 in Die Coss by ChristoffRudolff (14991545). He used (without the vinculum) for square roots. http://www.veling.nl/anne/templars/operation.html

Earliest Uses of Symbols of Operation and Grouping Last revision: Aug. 15, 1997 ADDITION AND SUBTRACTION SYMBOLS Plus (+) and minus (-). The plus symbol as an abbreviation for the Latin et (and), though appearing with the downward stroke not quite vertical, was found in a manuscript dated 1417 (Cajori). The + and - symbols first appeared in print in Mercantile Arithmetic or Behende und hubsche Rechenung auff allen Kauffmanschafft , by Johannes Widmann (born c. 1460), published in Leipzig in 1489. However, they referred not to addition or subtraction or to positive or negative numbers, but to surpluses and deficits in business problems (Cajori vol. 1, page 128). Cajori says, "There is clear evidence that, as a lecturer at the University of Leipzig, Widmann had studied manuscripts in the Dresden library in which + and - signify operations, some of these having been written as early as 1486." Johnson (page 144) says a series of notes from 1481, annotated by Widmann, contain the + and - symbols, and he asks whether Widman could have copied these symbols from some unknown professor at the University of Leipzig. Johnson also says that a student's notes from one of Widmann's 1486 lectures show the + and - signs. Giel Vander Hoecke used + and - as symbols of operation in Een sonderlinghe boeck in dye edel conste Arithmetica

92. ¥³.16¼¼±âÀÇ ÀÌÅ»¸®¾Æ ¼öÇÐ : ¸£³×»ó½ºÀÇ »ó¾÷¼� The summary for this Korean page contains characters that cannot be correctly displayed in this language/character set. http://my.netian.com/~martin93/math/history/his5.htm

ÀÌµé ±âÈ£´Â °è»ê¼úÀÇ ¾Æ¹öÁö¶ó°í ºÒ¸®¿ì´Â µ¶ÀÏÀÇ À§µå¸¸(John Widmann)ÀÌ 1489³â¿¡ ¶óÀÌÇÁÄ¡È÷¿¡¼­¹ßÇ¥Çß´ø »ê¼ö¥¿¡ ³À½À¸·Î ³ªÅ¸³­´Ù. ´ç½ °úºÎÁ·ÀÇ Àǹ̷Π½èÁö¸¸, Á¡Â÷ °¡¹ý°ú °¨¹ýÀ» ÀǹÌÇÏ´Â ±âÈ£·Î ¾²°Ô µÈ´Ù. 'Ç·¯½º'¶ó´Â Ç¥ÇöÀº ÀÌ ¥¿¡¼­ ¾²°í ÀÖÁö ¾ÊÁö¸¸ '¸¶À̳ʽº' ¶ó´Â ¸»Àº »ç¿ëµÇ°í ÀÖ´Ù. '+'±âÈ£´Â ¶óƾ¾î¿¡¼­ '¶Ç´Â'À̶ó´Â Àǹ̸¦ °®´Â et¸¦ »¡¸® ¾´ ÇüÅ¿¡¼­ ºñ·ÔµÈ °ÍÀÌ´Ù. ±×·¯³ª '-'±âÈ£ÀÇ ±â¿øÀº ¾Ë ¼ö ¾ø´Ù. ºó ´ëÇÐÀÇ ±³¼ö¿´´ø ½´¶óÀ̺£¸£(Heinrich Schreiber)´Â 1521³â¿¡ ¹ßÇ¥Çß´ø ¥¿¡¼­ +,-¸¦ µ¡¼À°ú »¬¼ÀÀÇ Àǹ̷Π»ç¿ëÇÏ¿´´Ù. ±×ÀÇ Á¦ÀÚ ·çµ¹ÇÁ(Christoff Rudolff)´Â 1525³â¿¡ ¹ßÇàµÈ ±×ÀÇ ´ë¼öÇÐ ¥¿¡¼­ +,-¿Ü¿¡µµ ±ÙÈ£ ¡î¸¦ ¾²°í ÀÖ´Ù. ±ÙÈ£¡î´Â ³À½ ¿¡´Â ´Ü¼øÈ÷ ¶ó°í ½è´Ù. ÀÌ°ÍÀº ±ÙÀ» ÀǹÌÇÏ´Â rootÀÇ ¸Ó¸® ±ÛÀÚ r·ÎºÎÅÍ ¿Ô´Ù´Â À̾߱⵵ ÀÖ´Ù. ÀÌ ±âÈ£´Â ¿µ¾î·Î ¾²¿©Áø ÖÊÀÇ ´ë¼öÇÐ¥À̶ó°í ¾Ë·ÁÁø ·¹ÄÚµå(Robert Recorde, ¾à 1510-1558)ÀÇ <ÁöÇýÀÇ ½¡µ¹, whestone of wittle, 1557> ½ºÀ§½º ¼öÇÐÀÚ ¶õ(Johann Heinrich Rahn)ÀÌ 1659³â¿¡ ò¸®È÷¿¡¼­ ¹ßÇàÇß´ø <´ë¼öÇÐ, Teutsche Algebra>

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