1. Medioevo In Rete - Personaggi Bhaskara (11141185). gherard of cremona (1114-1187). Ibn Yahya al-Maghribi Al-Samawal (1130-1180) http://indice.medioevo.ws/Personaggi/Matematici.htm

Home Database eventi Medioevo in rete Gruppi storici ... Contenuti speciali MEDIOEVO IN RETE INDICE SEGNALA UN SITO ENIGMAGALGANO Matematici del XII secolo Omar Khayyan (18 maggio 1048 - 4 dicembre 1131) Abraham bar Hiyya Ha-Nasi Adelard of Bath Abraham ben Meir ibn Ezra al-Ishbili Abu Muhammad Jabir ibn Aflah ... Torna ai personaggi Questa sezione è aggiornata e mantenuta da Maurizio Calì. inorbita@tiscalinet.it Medioevo.ws - Una finestra sul Medioevo Registrazione al Tribunale di Milano n. 683 del 30/11/01 Direttore editoriale Daniele Revelant - Direttore responsabile Luca Mascardi Responsabile contenuti storici Maurizio Calì Redazione : Via F.Nava 21, 20159 Milano Il portale non è collegato ai siti recensiti e non è responsabile del loro contenuto Si prega di leggere la nota informativa Informazioni sul sito Pubblicità Collabora ... Contatta la redazione

2. Linkkejä Abu Ja'far Muhammad ibn Musa AlKhwarizmi. gherard of cremona. Leonardo Pisano Fibonacci http://cc.oulu.fi/~pulkkine/linkit.html

Mathematics in Early Civilizations Muinaiskulttuurien matematiikasta Ancient Egyptian mathematics Egyptian mathematics ... Gerbert of Aurillac (ca. 955-1003) 2. Arabialaisista numeroista logaritmeihin Ancient Indian mathematics Aryabhata Brahmagupta Arabic/Islamic mathematics ... What on Earth is a Logarithm? 3. Astrolabista mekaaniseen laskukoneeseen An Ancient Greek Computer The Antikythera Mechanism: Physical and Intellectual Salvage from the 1st Century B.C. The Antikythera Mechanism Links The Antikythera Mechanism ... Curt Herzstark and his Pocket Calculator CURTA 4. Matemaattisista taulukoista Babbagen analyyttiseen koneeseen The Babbage Pages Charles Babbage Institute Who Was Charles Babbage? The Analytical Engine ... The ENIAC Story 7. Transistorista terakoneeseen Computers: From the Past to the Present A History of Computers Articles on the History of Electronic Calculators Laskulaitteista ja tietokoneista ... ASCI White

3. THABIT IBN QURRA some of his books were translated into Latin by gherard of cremona. In recent centuries, a number of his books have http://members.tripod.com/~wzzz/QURRA.html

Get Five DVDs for $.49 each. Join now. Tell me when this page is updated THABIT IBN QURRA (836-901 A.D.) Thabit Ibn Qurra Ibn Marwan al-Sabi al-Harrani was born in the year 836 A.D. at Harran (present Turkey). As the name indicates he was basically a member of the Sabian sect, but the great Muslim mathematician Muhammad Ibn Musa Ibn Shakir, impressed by his knowledge of languages, and realising his potential for a scientific career, selected him to join the scientific group at Baghdad that was being patronised by the Abbasid Caliphs. There, he studied under the famous Banu Musa brothers. It was in this setting that Thabit contributed to several branches of science, notably mathematics, astronomy and mechanics, in addition to translating a large number of works from Greek to Arabic. Later, he was patronised by the Abbasid Caliph al-M'utadid. After a long career of scholarship, Thabit died at Baghdad in 901 A.D. Thabit's major contribution lies in mathematics and astronomy. He was instrumental in extending the concept of traditional geometry to geometrical algebra and proposed several theories that led to the development of non-Euclidean geometry, spherical trigonometry, integral calculus and real numbers. He criticised a number of theorems of Euclid's elements and proposed important improvements. He applied arithmetical terminology to geometrical quantities, and studied several aspects of conic sections, notably those of parabola and ellipse. A number of his computations aimed at determining the surfaces and volumes of different types of bodies and constitute, in fact, the processes of integral calculus, as developed later.

4. Ahmed Biography of Ahmed ibn Yusuf (835912) proportion and it was translated into Latin by gherard of cremona. The book is largely a commentary on, and expansion http://sfabel.tripod.com/mathematik/database/Ahmed.html

Ahmed ibn Yusuf Born: 835 in Baghdad (now in Iraq) Died: 912 in Cairo, Egypt Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Ahmed ibn Yusuf wrote on ratio and proportion and it was translated into Latin by Gherard of Cremona. The book is largely a commentary on, and expansion of, Book 5 of Euclid 's Elements Ahmed ibn Yusuf also gave methods to solve tax problems which appear in Fibonacci 's Liber Abaci . He was also quoted by Bradwardine Jordanus and Pacioli References (2 books/articles) Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996

5. Gherard gherard of cremona. Born 1114 in Cremona, Italy Died 1187 in Toledo, Spain. Gherardof Cremona's name is often written as Gerard or sometimes Gerhard. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Gherard.html

Gherard of Cremona Born: 1114 in Cremona, Italy Died: 1187 in Toledo, Spain Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Gherard of Cremona 's name is often written as Gerard or sometimes Gerhard. After being educated in Italy, he realised that European education was narrow and that he decided that he would try to make the riches of Arabic science available to European scholars through Latin translations of the major works in Arabic. For this reason Gherard went to Toledo in Spain where his intention was to learn Arabic so he could read Ptolemy 's Almagest since no Latin translations existed at that time. Although we do not have detailed information of the date when Gherard went to Spain, he was certainly there by 1144. He remained there for most of the rest of his life and although he does not appear to have gathered a school around him, he certainly appears to have had quite a lot of assistance. He may have employed helpers who assisted him in the copying and checking of manuscripts and other chores associated with the great translation industry that he started. In all over a period of forty years, Gherard translated around eighty works from Arabic to Latin. The complete list of works which he translated is given in [1]. Some of these translations were of Arabic works while others were of Greek works which had been translated into Arabic. Often however, the works were a mixture in the sense that they were Arabic commentaries on Greek works.

6. Gherard Biography of Gherard (11141187) gherard of cremona. Born 1114 in Cremona, Italy. Died 1187 in Toledo, Spain http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Gherard.html

Gherard of Cremona Born: 1114 in Cremona, Italy Died: 1187 in Toledo, Spain Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Gherard of Cremona 's name is often written as Gerard or sometimes Gerhard. After being educated in Italy, he realised that European education was narrow and that he decided that he would try to make the riches of Arabic science available to European scholars through Latin translations of the major works in Arabic. For this reason Gherard went to Toledo in Spain where his intention was to learn Arabic so he could read Ptolemy 's Almagest since no Latin translations existed at that time. Although we do not have detailed information of the date when Gherard went to Spain, he was certainly there by 1144. He remained there for most of the rest of his life and although he does not appear to have gathered a school around him, he certainly appears to have had quite a lot of assistance. He may have employed helpers who assisted him in the copying and checking of manuscripts and other chores associated with the great translation industry that he started. In all over a period of forty years, Gherard translated around eighty works from Arabic to Latin. The complete list of works which he translated is given in [1]. Some of these translations were of Arabic works while others were of Greek works which had been translated into Arabic. Often however, the works were a mixture in the sense that they were Arabic commentaries on Greek works.

7. Chronology For 1100 To 1300 from Arabic. 1144 gherard of cremona begins translating Arabic works(and Arabic translations of Greek works) into Latin. 1149 Al http://www-gap.dcs.st-and.ac.uk/~history/Chronology/1100_1300.html

Chronology for 1100 to 1300 Previous page Chronology index Full chronology Next page ... Jabir ibn Aflah writes works on mathematics which, although not as good as many other Arabic works, are important since they will be translated into Latin and become available to European mathematicians. About 1140 Bhaskara II (sometimes known as Bhaskaracharya) writes Lilavati The Beautiful ) on arithmetic and geometry, and Bijaganita Seed Arithmetic ), on algebra. Adelard of Bath produces two or three translations of Euclid 's Elements from Arabic. Gherard of Cremona begins translating Arabic works (and Arabic translations of Greek works) into Latin. Al-Samawal writes al-Bahir fi'l-jabr The brilliant in algebra ). He develops algebra with polynomials using negative powers and zero. He solves quadratic equations, sums the squares of the first n natural numbers, and looks at combinatorial problems. Arabic numerals are introduced into Europe with Gherard of Cremona 's translation of Ptolemy 's Almagest . The name of the "sine" function comes from this translation. About 1200 Chinese start to use a symbol for zero. (See this

8. References For Gherard Gerson, Levi ben (268). gherard of cremona (668). Ghetaldi, Marino (235) http://www-history.mcs.st-and.ac.uk/References/Gherard.html

References for Gherard Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: H L L Busard, The Latin translation of the Arabic version of Euclid's 'Elements' commonly ascribed to Gerard of Cremona : Introduction, edition and critical apparatus (Leiden, 1984). Articles: History of mathematics (San Diego, CA, 1996), 173-205. Centaurus R Lemay, Gerard of Cremona, Dictionary of the Middle Ages (New York, 1983), 422-423. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 1999 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/Gherard.html

9. Untitled II, p. 233. gherard of cremona Born 1114 in Cremona, Italy Died 1187in Toledo, Spain. Gherard's name is sometimes written as Gerard. http://www.math.tamu.edu/~don.allen/history/mideval/mideval.html

Next: About this document Mideval Europe century The Europeans learned Arabic in the 12 century. All mathematics and astronomy was written in Arabic. By the end of the 12 century the best mathematics was done in Christian Italy. During this century there was a spate of translations of Arabic works to Latin. Later Example. Elements in Arabic Latin in 1142 by Adelard of Bath (ca. 1075-1160). He also translated Al-Khwarizmi's astronomical tables (Arabic Latin) in 1126 and in 1155 translated Ptolemy's Almgest (Greek Latin) (The world background at this time was the crusades.) Gherard of Cremona Born: 1114 in Cremona, Italy Died: 1187 in Toledo, Spain Gherard's name is sometimes written as Gerard. He went to Toledo, Spain to learn Arabic so he could read Ptolemy's Almagest since no Latin translations existed at that time. He remained there for the rest of his life. Gherard made translations of Ptolemy (1175) and of Euclid from Arabic. Some of these translations from Arabic became more popular than the (often earlier) translations from Greek. In making translations of other Arabic work he translated the Arabic word for sine into the Latin sinus, from where our

10. Biography-center - Letter G Getty, Francis E. whitemountainart.com/Biographies/bio_feg.htm; gherard of cremona,wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Gherard.html; http://www.biography-center.com/g.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 G 523 biographies www.pathfinder.com/time/time100/scientist/profile/godel.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Godel.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Gopel.html G.i., American www.pathfinder.com/time/time100/heroes/profile/gi01.html Gabbiani, Beppe www.grandprix.com/gpe/drv-gabbep.html Gabelich, Gary www.hickoksports.com/biograph/gabelichg.shtml Gable, Daniel M. www.hickoksports.com/biograph/gabledan.shtml Gabor, Dennis www.nobel.se/physics/laureates/1971/gabor-autobio.html Gachot, Bertrand www.grandprix.com/gpe/drv-gacber.html Gaddi, Taddeo www.kfki.hu/~arthp/bio/g/gaddi/taddeo/biograph.html Gadgil, Ashok web.mit.edu/invent/www/inventorsA-H/gadgil.html Gadgil, Ashok

11. - Great Books - contribution. He was known as Alkindus in Latin and a large number ofhis books were translated into Latin by gherard of cremona. His http://www.malaspina.com/site/person_716.asp

Kindi (al-) Sometimes called pre-eminently "The Philosopher of the Arabs " flourished in the 9th century, the exact dates of his birth and death being unknown. He was born in Kufa, where his father was governor under the Caliphs Mahdi and Harun al-RashId. His latter studies were made in Bagdad, where he remained, occupying according to some a government position. In the orthodox reaction under Motawakkil, when all philosophy was suspect, his library was confiscated, but he himself seems to have escaped. His writings - like those of other Arabian philosophers - are encyclopaedic and are concerned with most of the sciences; they are said to have numbered over two hundred, but fewer than twenty are extant. Some of these were known in the middle ages, for Kindi is placed by Roger Bacon in the first rank after Ptolemy as a writer on optics. His work De Somniorum Visione was translated by Gerard of Cremona and another was published as De medicinarum compositarum gradibus investigandis Libellus (Strassburg, 1531). He was one of the earliest translators and commentators of

12. Math Forum - Ask Dr. Math According to some sources, sinus first appears in Latin in a translationof the Algebra of alKhowarizmi by gherard of cremona (1114-1187). http://mathforum.org/library/drmath/view/54053.html

Associated Topics Dr. Math Home Search Dr. Math How the Trig Functions Got their Names Date: 12/14/97 at 03:42:57 From: Frank Becker Subject: How the Trig Functions got their names I can guess why three of the trig functions are called cosine, cotangent, and cosecant. But why were the other three named the sine, the tangent, and the secant? Does the choice of the words tangent and secant have anything to do with the ordinary geometric meaning of these words? Date: 12/14/97 at 05:59:08 From: Doctor Luis Subject: Re: How the Trig Functions got their names Have you tried a dictionary? (you'd be surprised to know the number of things you can find out by using one). Webster's New Collegiate Dictionary suggests the following etymologies: sine : Medieval Latin "sinus" from the Latin word for "curve" tangent: Latin "tangent-, tangens" from present participle of "tangere" (to touch) secant : New Latin "secant-, secans" from Latin present participle of "secare" (to cut) Webster's II International has, for sine: Latin sinus, a bend, gulf, bosom of a garment, used as translation of Arabic jayb, bosom of a garment, sine (in the latter sense from Sanskrit Jiva, bowstring, chord of an arc, sine). For more etymological information, see Jeff Miller's "Earliest Known Uses of Some of the Words of Mathematics: (S) http://members.aol.com/jeff570/s.html

13. Recent Articles In St Andrews Archive: How Do We Know About Greekmathematics? By in the 9th century. gherard of cremona translated the Thabit versioninto Latin in the 12th century. An earlier Latin translation http://mathforum.org/epigone/math-history-list/spythimpcrou

Recent Articles in St Andrews Archive: How do we know about Greekmathematics? by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to math-history-list Subject: Recent Articles in St Andrews Archive: How do we know about Greekmathematics? Author: xpolakis@otenet.gr Date: http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Greek_sources_1.html APH The Math Forum

14. - Great Books - some of his books were translated into Latin by gherard of cremona. In recent centuries, a number of his books have http://www.malaspina.com/site/person_968.asp

Thabit ibn Qurrah al-Harrani Thabit Ibn Qurra Ibn Marwan al-Sabi al-Harrani was born in the year 836 A.D. at Harran (present Turkey). As the name indicates he was basically a member of the Sabian sect, but the great Muslim mathematician Muhammad Ibn Musa Ibn Shakir, impressed by his knowledge of languages, and realising his potential for a scientific career, selected him to join the scientific group at Baghdad that was being patronised by the Abbasid Caliphs. There, he studied under the famous Banu Musa brothers. It was in this setting that Thabit contributed to several branches of science, notably mathematics, astronomy and mechanics, in addition to translating a large number of works from Greek to Arabic. Later, he was patronised by the Abbasid Caliph al-M'utadid. After a long career of scholarship, Thabit died at Baghdad in 901 A.D. Thabit's major contribution lies in mathematics and astronomy. He was instrumental in extending the concept of traditional geometry to geometrical algebra and proposed several theories that led to the development of non-Euclidean geometry, spherical trigonometry, integral calculus and real numbers. He criticised a number of theorems of Euclid's elements and proposed important improvements. He applied arithmetical terminology to geometrical quantities, and studied several aspects of conic sections, notably those of parabola and ellipse. A number of his computations aimed at determining the surfaces and volumes of different types of bodies and constitute, in fact, the processes of integral calculus, as developed later.

15. Enigma Galgano - Medioevo In Rete - Personaggi - Matematici Del XII Secolo Translate this page 6) Bhaskara (1114-1185). 7) gherard of cremona (1114-1187). 8) Ibn Yahya al-MaghribiAl-Samawal (1130-1180). 9) Sharaf al-Din al-Muzaffar al-Tusi (1135-1213). http://web.infinito.it/utenti/e/enigmagalgano/Medioevo_in_Rete/personaggi/matema

Matematici del XII secolo Omar Khayyan Leonardo Pisano Fibonacci Torna a Personaggi Omar Khayyan (18 maggio 1048 - 4 dicembre 1131) Abraham bar Hiyya Ha-Nasi Adelard of Bath Abraham ben Meir ibn Ezra al-Ishbili Abu Muhammad Jabir ibn Aflah ... Johannes de Sacrobosco

16. Mathem_abbrev Friedrich Gelfand, Israil Geminus Gemma Frisius, Regnier Genocchi, Angelo, Gerardof Cremona Gerhard of Cremona Germain, Sophie gherard of cremona Gibbs, Josiah http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm

Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive. Some suggestions on the historical perspective might be: (a) Any wars etc. (b) Scientific breakthroughs of the time (c) Major discoveries of the time (d) How did this mathematician change history etc.

17. ABU AL-QASIM AL-ZAHRAWI AlTasrif was first translated by gherard of cremona into Latin in theMiddle Ages. It was followed by several other editors in Europe. http://www.ummah.org.uk/history/scholars/ZAHRAWI.html

18. Euclid's Other Works It is probable that gherard of cremona (11141187) translated this edition intoLatin, and the work became well known because of this to the scholars of the http://www.math.sfu.ca/histmath/Europe/Euclid300BC/OTHERWORKS.HTML

Euclid's Other Works Phaenomena / Data / Optica / Catoptrica / Sectio Canonis / On Divisions / Pseudaria / Surface-Loci Title Page to L. Berggren's and R. Thomas's translation of Euclid's Phaenomena PHAENOMENA This is Euclidís astronomical work and is still available today. The Phaenomena is a book containing 18 propositions dealing with spherical geometry. It was perhaps written shortly after Autolycusís Moving Sphere , on the same subject, and another work entitled Spaerica , possibly compiled by Eudoxus . The Phaenomena deals with geometrical proofs of propositions which are established by observation, primarily dealing with the rising and setting of stars together or one after another, in a given order. It also contains ten propositions related to the problem of determining the length of daylight on a given day at a given locality. DATA The focus of the Data is concerned with the first six books of the Elements ; it is often considered a supplement. This is a collection of geometrical theorems and ninety-six exercises (many editions contain a different number of exercises, usually in agreement around 94) intended to allow the reader to gain a better knowledge of solving problems. The Data is considered appropriate to one of the goals of Greek mathematics, namely, the solution of new problems. This manual contains propositions concerning certain given or determined magnitudes, and from this other magnitudes can also be determined.

19. OPE-MAT - Historique Translate this page Fabri, Honoré Francoeur, Louis Germain, Sophie Fagnano, Giulio Frank, Philippgherard of cremona Fagnano, Giovanni Franklin, Philip Ghetaldi, Marino Fano http://www.gci.ulaval.ca/PIIP/math-app/Historique/mat.htm

A Abel , Niels Akhiezer , Naum Anthemius of Tralles Abraham bar Hiyya al'Battani , Abu Allah Antiphon the Sophist Abraham, Max al'Biruni , Abu Arrayhan Apollonius of Perga Abu Kamil Shuja al'Haitam , Abu Ali Appell , Paul Abu'l-Wafa al'Buzjani al'Kashi , Ghiyath Arago , Francois Ackermann , Wilhelm al'Khwarizmi , Abu Arbogast , Louis Adams , John Couch Albert of Saxony Arbuthnot , John Adelard of Bath Albert , Abraham Archimedes of Syracuse Adler , August Alberti , Leone Battista Archytas of Tarentum Adrain , Robert Albertus Magnus, Saint Argand , Jean Aepinus , Franz Alcuin of York Aristaeus the Elder Agnesi , Maria Alekandrov , Pavel Aristarchus of Samos Ahmed ibn Yusuf Alexander , James Aristotle Ahmes Arnauld , Antoine Aida Yasuaki Amsler , Jacob Aronhold , Siegfried Aiken , Howard Anaxagoras of Clazomenae Artin , Emil Airy , George Anderson , Oskar Aryabhata the Elder Aitken , Alexander Angeli , Stefano degli Atwood , George Ajima , Chokuyen Anstice , Robert Richard Avicenna , Abu Ali B Babbage , Charles Betti , Enrico Bossut , Charles Bachet Beurling , Arne Bouguer , Pierre Bachmann , Paul Boulliau , Ismael Bacon , Roger Bhaskara Bouquet , Jean Backus , John Bianchi , Luigi Bour , Edmond Baer , Reinhold Bieberbach , Ludwig Bourgainville , Louis Baire Billy , Jacques de Boutroux , Pierre Baker , Henry Binet , Jacques Bowditch , Nathaniel Ball , W W Rouse Biot , Jean-Baptiste Bowen , Rufus Balmer , Johann Birkhoff , George Boyle , Robert Banach , Stefan Bjerknes, Carl

20. Virtual Encyclopedia Of Mathematics karl friedrich gelfond aleksandr osipovich gellibrand henry geminus gentzen gerhardgergonne joseph diaz germain sophie gherard of cremona ghetaldi marino http://www.lacim.uqam.ca/~plouffe/Simon/supermath.html

Super-Index of Biographies of Mathematicians abel niels henrik abraham bar hiyya ha-nasi abraham max abu kamil shuja ibn aslam ibn muhammad ... zygmund antoni This index was automatically generated using a new tagging program written by Simon Plouffe at LaCIM

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