61. Un Altra Dimostrazione Semplicissima. Translate this page scheda3_1.gif, La dimostrazione di thabit ibn qurra. La dimostrazione seguenteè attribuita al matematico arabo thabit ibn qurra (826-901). http://www2.math.unifi.it/~archimede/archimede/pitagora/exh_pitagora/scheda3.htm

Un'altra dimostrazione semplicissima. dimostrazione visiva e spiegazione di Airy dimostrazione di Thabit Ibn Qurra La Sembra I am, as you may see, a + b When two triangles on me stand, But if I stand on them instead, The squares of both sides are read. Mi presento, signori, eccomi qui: a + b Con due triangoli sopra, chiedo scusa* Ma se questi di sotto stanno quieti Si formano i quadrati dei cateti. *Di "chiedo scusa", amici, chiedo scusa, non ho la rima dell’ipotenusa ... La dimostrazione di Thabit Ibn Qurra.

62. Timeline Around 850 thabit ibn qurra made a number of important discoveries in numbertheory and wrote Book on the determination of amicable numbers which contained http://www.mathsisgoodforyou.com/timeline.htm

timeline home courses topics theorems ... timeline Around 30 000BC to 5000BC. We have the findings of some kind of mathematical pursuit, from recording the number on bones, to early geometrical designs. Around 4000BC to 2000BC. Babylonians and Egyptians developed calendars and began using them. Around 1900BC one of the two mathematical papyri is written - the Moscow Papyrus (also called the Golenishev papyrus) giving details of Egyptian geometry. Between 1850 and 1750BC Babylonians know of and use what we now call Pythagoras' theorem. They also compiled tables of square and cube roots. About 1700BC the Ahmes (or Rhind) papyrus is written. It shows number work of Egyptian scribe, in particular dealing with fractions. Around BC Thales of Miletus develops an abstract geometry, elevating it from the measurement of surfaces and solids to the first use of logical proof. If at all, Pythagoras of Samos lived sometimes between 50 th and the 52 nd Olympiads, or between 580 and 568 BC. He founded a school at Crotona , teaching that numbers are the cause of the various qualities of everything that surrounds us About 450BC Greeks begin to use written numerals and Zeno presented his paradoxes 387BC Plato founds his Academy in Athens. Plato thought that there was an ideal world in which ideas of everything that exist in our world are created. We try to re-create these ideas in our everyday world by creating things, but they can never be as perfect as the 'ideals' of these things. He identified five regular polyhedra, which are now called

63. Tahbit Ib Qura Jerusalem, The Magnes Press, 2000 423429. Verza. qurra, thabit ibn.Ouvres D’Astronomie, trad. Régis Morelon, Belles Lettres, Paris, 1987. Verza http://planeta.terra.com.br/arte/casadasabedoria/filislam/autores/qura.htm

Carmody, Francis J. Notes on the Astronomical Works of Thâbit b. Qurra, Isis: an International Review Devoted to the History of Science and its Cultural Influences , Official Quartely Journal of the History of Science Society, vol. 46, part 3, no. 145, 1955: 235-242. [Verza] Griffith. Theodore Abu Qurrah's Arabic Tract on the Christian Practice of Venerating Images. Journal of the American Oriental Society, Vol. 105, No. 1. (Jan. - Mar., 1985), pp. 53-73.[pdf] [verza] Pines, Sholomo. Thabit B. Qurra’s conception of number and theory of the Mathematical Infinite. In: The Collected Works of Sholomo Pines , vol. II (Studies in Arabic Versions of Greek texts and in Mediaeval Science), Jerusalem, The Magnes Press, 2000: 423-429. [Verza] Qurra, Thabit ibn. Ouvres D’Astronomie , trad. Régis Morelon, Belles Lettres, Paris, 1987. [Verza]

64. La Matematica Del Mondo Islamico Translate this page nuova dimostrazione del teorema di thabit ibn qurra introducendo importanti nuove e che forse era stato scoperto dallo stesso di thabit ibn qurra. http://www.arab.it/islam/la_matemtica_del_mondo_islamico.htm

La matematica del mondo islamico * Home Arte e Cultura Immigrazione Islam ... E - Mail Gli Arabi, ovvero i matematici del mondo islamico che vissero tra il nono e il quindicesimo secolo, non furono semplici traduttori degli scritti greci di matematica, ma, come dimostrano studi recenti, elaborarono molte parti della matematica che poi ricomparve in Europa tra il Cinquecento e il Settecento. Sino a tempi recenti la maggior parte degli storici della matematica conti nuano a rifiutare l'ipotesi di qualsiasi contributo originale del mondo islamico allo sviluppo della matematica sia omettendo di riportare le loro scoperte sia accettando quasi acriticamente l'opinione del filosofo della scienza Pierre Maurice Duhem per cui la scienza araba non avrebbe fatto altro che riprodurre quanto le era pervenuto dalla traduzione dei matematici dell' antica Grecia e consegnarlo ai matematici europei. In questo modo, il cammino della scienza, in particolare della matematica, si sarebbe interrotto per circa 1000 anni, per poi riprendere dal punto in cui i Greci l'avevano lasciata. Unione sovietica francobollo commemorativo con il nome Abu Abdullah Muhammad Bin Musa Al-khwarizmi "1200 anni"

65. Saudi Aramco World : Science:The Islamic Legacy: Science In The Golden Age The Banu Musa and thabit ibn qurra and his sons did not work in isolation.The works that issued from the House of Wisdom were the product of many different http://www.saudiaramcoworld.com/issue/198203/science.the.islamic.legacy-science.

May/June 1982 Volume 33, Number 3 May/June 1982 Volume 33, Number 3 Science:The Islamic Legacy Science in the Golden Age Written by Paul Lunde Illustrated by Michael Grimsdale Additional illustrations courtesy of Bodleian Library Towards the end of the 10th century, Ibn al-Nadim, son of a Baghdad , bookseller and boon companion of Abbasid caliphs, compiled an annotated bibliography of books that had passed through his hands during the course of his long and active life. The sheer number of books that he lists, to say nothing of the range of their subject matter, is astonishing: Aristotle appears beside Sindbad the Sailor, Euclid beside the stories of Goha, Plato beside the poems of'Antar ibn Shad-dad. The most striking feature of Ibn al-Nadim's catalog, however, is the number of books dealing with science. In a chapter entitled The Reason Why Books on Philosophy and Other Ancient Sciences Became Plentiful in This Country, Ibn al-Nadim relates a strange story of how Aristotle appeared in a dream to the Caliph al-Ma'mun and assured him that there was no conflict between reason and revelation. Thus reassured, al-Ma'mun set about obtaining the works of the Greek philosophers, the first step toward founding the famous House of Wisdom, a center for the translation of Greek scientific works into Arabic. Ibn al-Nadim told the story this way: This dream was one of the most definite reasons for the output of books. Between al-Ma'mun and the Byzantine emperor there was correspondence ... so al-Ma'mun wrote to the Byzantine emperor asking his permission to obtain a selection of old scientific manuscripts, stored and treasured in the country of the Byzantines. After first refusing, he finally complied, and al-Ma'mun sent forth a number of scholars, among them al-Hajjaj ibn Matar, Ibn al-Batrik, Salman, the director of the House of Wisdom and many others. They selected books from those they found and brought them back to al-Ma'mun, who ordered them to prepare translations of them.

66. The University Of Illinois At Chicago Department Of Classics And Mediterranean S With Amos Bertolacci, thabit ibn qurra s Concise Exposition of Aristotle sMetaphysics Text, Translation, Commentary, in thabit ibn qurra, http://www.uic.edu/las/clas/David_Reisman.html

Previous Faculty List Next David C. Reisman , BA, MA (1993, Boston University), PhD (2001, Yale University) Assistant Professor of Arabic-Islamic Thought Areas of Research and Publication: Medieval Arabic-Islamic Philosophy (particularly Avicenna and the Avicennan Tradition); Graeco-Arabic translation movement in medieval Islam (social and political contexts); Arabic history and historiography (Mamluk period); Arabic codicology and paleaography; medieval Arabic grammar and literary theory. Recent Publications: The Making of the Avicennan Tradition: The Transmission, Contents, and Structure of Ibn Sina's al-Mubahathat (The Discussions) , Leiden: Brill, 2002. "Avicenna at the ARCE," in R. Wisnovsky, ed. Aspects of Avicenna (Princeton Papers: Interdiscplinary Journal of Middle Eastern Studies, vol. 10), Princeton, N.J.: Markus Wiener, 2000, pp. 131-182. "Miskawayh's Ethics in Andalus? (Philologica Arabica I)," Yale University Library Gazette , Supplement 4 (1999), pp. 1-7. "Ibn al-Athir,"

67. Muslim Contribution To Science 826 901 ibn qurra, thabit; mathematician. 865- 923 Razi, al- (Rhazes); alchemist,philosopher, physician. 839- 923 Tabari, al-; historian, theologian. http://www.umr.edu/~msaumr/reference/articles/science/contributors.html

Muslim Contribution to Science Muslim Contribution to Science

68. SCIENZA ARABA Moesgaard,thabit ibn qurra between Ptolemy and Copernicus a Analysis of http://www.dismec.unige.it/testi/cosmo/Theb.htm

SCIENZA ARABA THABIT IBN QURRA, 221/836-288/901 Da Règis Morellon, Introduzione Matematico eccellente e medico apprezzato al suo tempo fu un celebre traduttore dal greco all'arabo, e revisionò i testi derivanti dal siriaco, essendo questa la sua lingua materna. Le fonti arabe non sono concordi nell'indicare l'anno della nascita. Originario di Harran, in Mesopotamia, era membro della setta dei Sabei, presso i quali si erano conservate vive le tradizioni ellenistiche. Questa regione era anche famosa per la costruzione degli astrolabi. In seguito a dissapori con i correligionari si trasferì a Bagdad su invito di Muhammad b. Musa b. Shakir, entrando nel circolo scientifico da lui fondato assieme ai suoi due fratelli. L'opera di Thabit b. Qurra si inserisce nel grande movimento scientifico che iniziò sotto l'impulso di al-Ma'mun che regnò dal 198/813 al 218/833. Sotto il suo regno furono costruiti due osservatori, uno a Damasco e l'altro a Bagdad e ampliò la famosa "Casa della sapienza" bayt al-hikma , un istituzione fondata sotto il regno di al-Mansur: era nello stesso tempo biblioteca generale, centro di ricerca e di traduzione dal siriaco o dal greco all'arabo. Accanto a questa istituzione operava nello stesso periodo il circolo fondato dai mecenati "fratelli Musa".

69. Storia Della Scienza-Indice Generale Translate this page SCIENZA ARABA. thabit ibn qurra, 221/836-288/901 di Astronomia tolemaica diAl-Fargani, un astronomo della generazione precedente a thabit ibn qurra. http://www.dismec.unige.it/testi/cosmo/Theb11.htm

SCIENZA ARABA THABIT IBN QURRA, 221/836-288/901 La misura della precessione La critica a Tolomeo dalla traduzione di Régis Morelon di Sull'anno solare di Thabit Ibn Qurra, Oeuvres astronomiques pag.30,8-17: "Dato ciò che abbiamo detto, è necessario che il movimento della sfera delle stelle fisse sia connesso a quello dell'orbita del sole, quanto alla leggera differenza che interviene tra il risultato che abbiamo trovato per lo spostamento dell'apogeo del sole, nel tempo che va dall'osservazione degli antichi alla nostra osservazione, essa deriva da un errore di osservazione. La prova di ciò risiede nel fatto che quando Tolomeo ha fatto la sintesi dei suoi risultati, ha menzionato che il movimento della sfera delle stelle fisse era di 1 grado per secolo,mentre noi abbiamo trovato che il movimento della sfera delle stelle fisse è di un grado e mezzo per secolo circa.". Questo passo è fondamentale perchè mostra come ben presto a Bagdad si mise a controllo i dati e i modelli di Tolomeo, mentre in Occidente si continuava a seguire l'astronomo greco, come Dante espressamente ancora riferisce nella Vita Nova e nel Convivio ,citando il compendio di Astronomia tolemaica di Al-Fargani, un astronomo della generazione precedente a Thabit Ibn Qurra. Per essere precisi la costante annuale di precessione trovata da Thabit è di 0;0,49,39, molto vicina alla misura di 50" per anno della tradizione sapienziale dell'antichità.

70. Recherche : Théorème%20de%20Thabit-Ibn%20Qurra thabit-ibn qurra , Certification IDDN. Dans les fiches,Parmi les mots-clés. 1 fiche trouvée . 2002 Collection M / Sciences http://publimath.univ-lyon1.fr/cgi-bin/publimath.pl?r=théorème de Thabit-Ibn Q

71. Proof Of The Preservation Of The Quran Many Quranic memorizers (qurra) were present during the lifetime of the Some people visited Zaid ibn thabit (one of the scribes of the Prophet) and http://www.themodernreligion.com/basic/quran/quran_proof_preservation.htm

Proof of The Preservation of the Quran By Sabeel Ahmed, while writing this article, the author is (E-mail: chooseislam@yahoo.com ) is at the final stage of his medical programme in Ross University, New York. He is the Co-chairman of the Da'wa Committee and Board of Director at the Muslim Community Center Masjid (the largest mosque in the Illinois state). He is also a member of the Islamic Circle of North America (ICNA) where he is actively involved in the 'toll free da'wa hotline' 1-800-662-islam, having first hand experience in handling calls by non-Muslim. He was a student of Shaykh Ahmed Deedat and his main field of interest is in comparative religion. There are hundreds of religions flourishing around the world: Christianity, Islam, Buddhism, Sikhism, Hinduism, Judaism, Bahaism, Babism, Zoroastrianism, Mormonism, Jehovas Witnesses, Jainism, Confucianism etc. And each of these religions claim that their scripture is preserved from the day it was revealed (written) until our time. A religious belief is as authentic as the authenticity of the scripture it follows. And for any scripture to be labeled as authentically preserved it should follow some concrete and rational criteria.

72. Thabit ReviewsR. Morélon, thabit ibn qurra. Oeuvres d astronomie. Paris 1987. In Zeitschriftfür Geschichte der ArabischIslamischen Wissenschaften 5, (1987) 274-279. http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Thabit.html

Al-Sabi Thabit ibn Qurra al-Harrani Born: 836 in Harran, Mesopotamia (now Turkey) Died: 18 Feb 901 in Baghdad, (now in Iraq) Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Thabit ibn Qurra was a native of Harran and a member of the Sabian sect. The Sabian religious sect were star worshippers from Harran often confused with the Mandaeans (as they are in [1]). Of course being worshipers of the stars meant that there was strong motivation for the study of astronomy and the sect produced many quality astronomers and mathematicians. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thabit ibn Qurra's native language, but he was fluent in both Greek and Arabic. Some accounts say that Thabit was a money changer as a young man. This is quite possible but some historians do not agree. Certainly he inherited a large family fortune and must have come from a family of high standing in the community.

73. Muslim Contributions To Science, Philosophy, And The Arts In the field of Algebra the Muslims continued with thabit ibn qurra s more 826 901 ibn qurra, thabit; mathematician. 865- 923 Razi, al- (Rhazes); http://www.jannah.org/articles/contrib.html

Back to Path to Islam ... Back to Path to Islam ...

74. The Mathematics Of Islam, Part 2 We focused on alKhwarizmi (750-850), thabit ibn qurra (830-890), Abu-Sahlal-Kuhi (early 900s), and ibn al-Haytham (965-1039). We concentrated on problems http://public.csusm.edu/DJBarskyWebs/330CollageOct01.html

The Mathematics of Islam, Part 2 The presentation given today by Dr. Barsky generated an overall theme that the works of the mathematicians of Islam during the period of (965-1039) seemed to show traces of calculus, despite the fact that calculus came about later in time. In this lecture, the topics consisted of al-Khwarizmi (750-850), Thabit ibn Qurra (830-890), Abu-Sahl al-Kuhi (early 900s), ibn al-Haytham (965-1039), Mohammed's Flight from Mecca (622), the Battle of Tours (732), the period of Caliphates, the Fall of Baghdad to Seljuk Turks (1055), the beginning of the first Crusade (1096), the arrival of the Mongols under Ghengis Khan (early 1200s), al-Khwarizmi's truncated pyramid problem, Mishnat ha-Middot, and ibn al-Haytham's volume of a paraboloid calculations. We did not have a mathematician of the day, instead we talked about our papers that will be due October 8. We then covered more of the history of Islamic mathematics. We focused on al-Khwarizmi (750-850), Thabit ibn Qurra (830-890), Abu-Sahl al-Kuhi (early 900s), and ibn al-Haytham (965-1039). We concentrated on problems from al-Khwarizmi and ibn al-Haytham, which mainly dealt with finding volumes. I really enjoyed the lecture about the volume of a parabola from ibn al-Haytham. I have previously seen the symbol for (the sum of), but I usually stopped at that point because I did not understand, or I felt like it was too complicated. I understand the logic behind finding the circumscribed volume, and inscribed volume of the parabola. I can see that the difference between the two is the volume of the bottom disk of the circumscribed volume. I see that the (sum symbol) is included in equations that are interested in finding the sum of the differences between two estimates which will give you the solution to a problem. I also see that as you take the sum of the differences you are reaching the limit which is related to the volume of the parabola.

75. PORTRAITS OF SCIENCE: A Polymath In The 10th Century -- Rashed 297 (5582): 773 - Scholars such as Banu Musa, thabit ibn qurra, Ibrahim ibn Sinan, alQuhi (1),and ibn Sahl measured curved surfaces and solids, invented new geometrical http://www.sciencemag.org/cgi/content/full/297/5582/773

Previous Article Table of Contents Next ... Article Science , Vol 297, Issue 5582, 773 , 2 August 2002 Summary of this Article PDF Version of this Article E-Letters: Submit a response to this article Download to Citation Manager Alert me when: new articles cite this article Search for similar articles in: Science Online ISI Web of Science PubMed Search Medline for articles by: Rashed, R. Request permission to use this article This article appears in the following Subject Collections: Essays Physics, Applied ADVERTISEMENT What's This... [DOI: 10.1126/science.1074591] Essays on Science and Society Also see the archival list of the Essays on Science and Society. PORTRAITS OF SCIENCE: A Polymath in the 10th Century Roshdi Rashed Ibn al-Haytham (10 to 11th century A.D.) T he turn of the first millennium was a time of intense research in mathematics, physics, and astronomy. One scientist active and productive in all of these fields was Ibn al-Haytham, called by his successors of the 12th century "Ptolemy the Second." Ibn al-Haytham, also known as Alhazen (the Latin transliteration of his first name al-Hasan), was born in Iraq, most likely in Bassorah, in the second half of the 10th century. He arrived in Cairo under the reign of Fatimid Caliph al-Hakim, a patron of the sciences who was particularly interested in astronomy. Ibn al-Haytham proposed to the Caliph a hydraulic project to control the flow of the Nilean early Aswan dam. The Caliph refused, but al-Haytham continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, until his death after 1040.

76. Background_Reading_and_Quiz thabit ibn qurra translated the Almagest of Ptolemy into Arabic in the 12th century.T or F? In Islamic culture, fields of learning were divided into two http://homepage.mac.com/kvmagruder/hsci/07-Islamic/background.html

HOME Announcements Exhibits Online EZBoard ... Kerry Magruder History of Science Online Course Info Time tips Semester Schedule Weekly Assignments ... Week 7: Islamic and Early Medieval Science Background Reading and Quiz Due Date Pts Activity Time Wednesday 11:59 p.m. Background Reading + Background Quiz Without a sense of context, history is anachronistic. 2 hrs. Without a doubt, there were more scientists in the middle ages than in antiquity, and many of them wrote in Arabic. We will spend the next three weeks getting to know a few of them. Background readings for this week: David Lindberg, Beginnings of Western Science , Chapter 8, "Science in Islam," pp. 162-182. Supplementary notes by Kerry Magruder (includes timeline). BACKGROUND QUIZ: The statements are either True or False. When you take the quiz at , you will see 15 of these statements, chosen at random. You can take the quiz a total of two times, up until the due date, when the quiz will no longer be available. If you take the quiz a second time, your first attempt will be erased and your second attempt will be recorded. You will find the quiz in the Quizzes section of Desire2Learn.

77. BiViO - Gli Autori not identified (1). Hunayn ibn Ishaq. Physica (1). ibn qurra, thabit.De imaginibus (1). ibn Wahsiyya, Abu Bakr Ahmad b. Ali alKasdani http://www.bivionline.it/en/PicatrixCitList_authors.html

index search quotations(58) illustrations works of the same author editions Authors -> Ignoto -> Picatrix -> Citations Citations author mentioned work not identified ( Al-Istamahis ( Al-Istamatis ( Bustan al-hukama' wa-qa'idat al-hikma ( ... Liber imaginum signorum ( Apollonio di Tiana (Pseudo) De secretis naturae ( Aristotele De anima ( Aristotele (Pseudo) Secretum secretorum ( Enoch Liber de quindecim stellis ( Fakhr ad-Din ar-Razi, Muhammad ibn Umar ibn al-Husain Al-sirr al-maktum ( Geber not identified ( Hunayn Ibn Ishaq Physica ( Ibn Qurra, Thabit De imaginibus ( Ibn Wahsiyya, Abu Bakr Ahmad b. Ali al-Kasdani Filaha al-nabatiyya ( Ibn al-Athir, Izz al-Din al-Kamil ( Muhammad Qur'an ( Pitagora not identified ( Shahrastani, Muhammad Ibn Abd Al-Karim Al-Milal wa-l-Nahal ( Tolomeo (Pseudo) Centiloquium ( al-Farabi, Abu Nasr Muhammad Ara'ahl al-madina al-fadila. ( al-Mutanabbi, Abu al-Tayyib Ahmad ibn al-Husayn Diwan ( al-Razi, Abu-Bakr Muhammad ibn Zakariya not identified (

78. BiViO - Proposte Di Lettura Translate this page luogo non identificato (1). Hunayn ibn Ishaq. Physica (1). ibn qurra, thabit.De imaginibus (1). ibn Wahsiyya, Abu Bakr Ahmad b. Ali al-Kasdani http://www.bivionline.it/it/PicatrixCitList_sections.html

indice cerca citazioni(58) illustrazioni opere stessa sezione edizioni Proposte di lettura -> Magia ed Ermetismo -> Ignoto - Picatrix -> Citazioni Citazioni autore opera citata luogo non identificato ( Al-Istamahis ( Al-Istamatis ( Bustan al-hukama' wa-qa'idat al-hikma ( ... Liber imaginum signorum ( Apollonio di Tiana (Pseudo) De secretis naturae ( Aristotele De anima ( Aristotele (Pseudo) Secretum secretorum ( Enoch Liber de quindecim stellis ( Fakhr ad-Din ar-Razi, Muhammad ibn Umar ibn al-Husain Al-sirr al-maktum ( Geber luogo non identificato ( Hunayn Ibn Ishaq Physica ( Ibn Qurra, Thabit De imaginibus ( Ibn Wahsiyya, Abu Bakr Ahmad b. Ali al-Kasdani Filaha al-nabatiyya ( Ibn al-Athir, Izz al-Din al-Kamil ( Muhammad Qur'an ( Pitagora luogo non identificato ( Shahrastani, Muhammad Ibn Abd Al-Karim Al-Milal wa-l-Nahal ( Tolomeo (Pseudo) Centiloquium ( al-Farabi, Abu Nasr Muhammad Ara'ahl al-madina al-fadila. ( al-Mutanabbi, Abu al-Tayyib Ahmad ibn al-Husayn Diwan ( al-Razi, Abu-Bakr Muhammad ibn Zakariya luogo non identificato (

79. Math Words Page 13 thabit ibn qurra discovered, and proved, a rule for creating amicable pairs in the AlFarisi (born 1260) gave a new proof of thabit ibn qurra s theorem, http://www.pballew.net/arithm13.html

Math Words, pg 13 Back to Math Words Alphabetical Index Aliquot parts of a number are proper divisors of the number that are smaller than the number. The aliquot parts of six are one, two, and three. The word joins two unlikely partners, the Latin ali for "other" and quot for how many. Together they came to mean a part of something, in this case, a part of the number of which it is a factor. The "other" meaning of ali remains today in words like alius, alibi, and alien. The quot root remains in quotient. Aliquot chains, sometimes called sociable chains , are formed by taking the sum of the aliquot parts and adding them to form a new number, then repeating this process on the next number. For some numbers, the result will bring you directly back to the original number. In that case the two numbers are called amicable numbers . For example, 220 and 284 are amicable numbers. The divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 and if you add all these numbers together, you can see they sum to 284. The aliquot parts of 284 are 1, 2, 4, 71, 142 and these sum to 220. The relationship between 220 and 284 was known at least as far back as Pythagorus (500 BC). Sam Kutler has written to tell me that the first use of a term like "friend" for the pair was in a commentary on the work of Nicomachus by Iamblichus, around 300 AD. He also thought the Greek term was

80. Untitled Abu lHasan thabit ibn qurra Born 826 in Harran, Mesopotamia (now Turkey) Died18 Feb 901 in Baghdad, (now in Iraq). tex2html_wrap_inline191 thabit was a http://www.math.tamu.edu/~don.allen/history/arab/arab.html

Next: About this document Arab Contributions Within a century of Muhammad's conquest of Mecca, Islamic armies conquered lands from northern Africa, southern Europe, through the Middle East and east up to India. Within a century of that the Caliphate split up into several parts. The eastern segment, under the Abbasid caliphs, became a center of growth, of luxury, and of peace. In 766 the caliph al-Mansur founded his capitol in Baghdad and the caliph Harun al-Rashid, established a library. The stage was set for his successor, Al-Ma'mum. In the 9 century Al-Ma'mum established Baghdad as the new center of wisdom and learning. He establihed a research institute, the Bayt al-Hikma (House of Wisdom), which would last more than 200 years. Al-Ma'mum was responsible for a large scale translation project of as many ancient works as could be found. Greek manuscripts were obtained through treaties. By the end of the century, the major works of the Greeks had been translated. In addition, they learned the mathematics of the Babylonnians and the Hindus. What follows is a brief introduction to a few of the more prominent Arab mathematicians, and a sample of their work

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