Aristotle's Physics
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Texts in Transit in the Medieval Mediterranean
Texts in Transit in the medieval mediterranean Edited by Y. Tzvi Langermann and Robert G. Morrison Texts in Transit in the Medieval Mediterranean Texts in Transit in the Medieval Mediterranean Edited by Y. Tzvi Langermann and Robert G. Morrison Th e Pennsylvania State University Press University Park, Pennsylvania This book has been funded in part by the Minerva Center for the Humanities at Tel Aviv University and the Bowdoin College Faculty Development Committee. Library of Congress Cataloging- in- Publication Data Names: Langermann, Y. Tzvi, editor. | Morrison, Robert G., 1969– , editor. Title: Texts in transit in the medieval Mediterranean / edited by Y. Tzvi Langermann and Robert G. Morrison. Description: University Park, Pennsylvania : The Pennsylvania State University Press, [2016] | Includes bibliographical references and index. Summary: “A collection of essays using historical and philological approaches to study the transit of texts in the Mediterranean basin in the medieval period. Examines the nature of texts themselves and how they travel, and reveals the details behind the transit of texts across cultures, languages, and epochs”— Provided by Publisher. Identifiers: lccn 2016012461 | isbn 9780271071091 (cloth : alk. paper) Subjects: lcsh: Transmission of texts— Mediterranean Region— History— To 1500. | Manuscripts, Medieval— Mediterranean Region. | Civilization, Medieval. Classification: lcc z106.5.m43 t49 2016 | ddc 091 / .0937—dc23 lc record available at https:// lccn .loc .gov /2016012461 Copyright © 2016 The Pennsylvania State University All rights reserved Printed in the United States of America Published by The Pennsylvania State University Press, University Park, PA 16802–1003 The Pennsylvania State University Press is a member of the Association of American University Presses. -
AL-KINDI 'Philosopher of the Arabs' Abū Yūsuf Yaʿqūb Ibn Isḥāq Al
AL-KINDI ‘Philosopher of the Arabs’ – from the keyboard of Ghurayb Abū Yūsuf Ya ʿqūb ibn Is ḥāq Al-Kindī , an Arab aristocrat from the tribe of Kindah, was born in Basrah ca. 800 CE and passed away in Baghdad around 870 (or ca. 196–256 AH ). This remarkable polymath promoted the collection of ancient scientific knowledge and its translation into Arabic. Al-Kindi worked most of his life in the capital Baghdad, where he benefitted from the patronage of the powerful ʿAbb āssid caliphs al- Ma’mūn (rg. 813–833), al-Muʿta ṣim (rg. 833–842), and al-Wāthiq (rg. 842–847) who were keenly interested in harmonizing the legacy of Hellenic sciences with Islamic revelation. Caliph al-Ma’mūn had expanded the palace library into the major intellectual institution BAYT al-ḤIKMAH (‘Wisdom House ’) where Arabic translations from Pahlavi, Syriac, Greek and Sanskrit were made by teams of scholars. Al-Kindi worked among them, and he became the tutor of Prince A ḥmad, son of the caliph al-Mu ʿtasim to whom al-Kindi dedicated his famous work On First Philosophy . Al-Kindi was a pioneer in chemistry, physics, psycho–somatic therapeutics, geometry, optics, music theory, as well as philosophy of science. His significant mathematical writings greatly facilitated the diffusion of the Indian numerals into S.W. Asia & N. Africa (today called ‘Arabic numerals’ ). A distinctive feature of his work was the conscious application of mathematics and quantification, and his invention of specific laboratory apparatus to implement experiments. Al-Kindi invented a mathematical scale to quantify the strength of a drug; as well as a system linked to phases of the Moon permitting a doctor to determine in advance the most critical days of a patient’s illness; while he provided the first scientific diagnosis and treatment for epilepsy, and developed psycho-cognitive techniques to combat depression. -
On the Use of Coptic Numerals in Egypt in the 16 Th Century
ON THE USE OF COPTIC NUMERALS IN EGYPT IN THE 16 TH CENTURY Mutsuo KAWATOKO* I. Introduction According to the researches, it is assumed that the culture of the early Islamic period in Egypt was very similar to the contemporary Coptic (Qibti)/ Byzantine (Rumi) culture. This is most evident in their language, especially in writing. It was mainly Greek and Coptic which adopted the letters deriving from Greek and Demotic. Thus, it was normal in those days for the official documents to be written in Greek, and, the others written in Coptic.(1) Gold, silver and copper coins were also minted imitating Byzantine Solidus (gold coin) and Follis (copper coin) and Sassanian Drahm (silver coin), and they were sometimes decorated with the representation of the religious legends, such as "Allahu", engraved in a blank space. In spite of such situation, around A. H. 79 (698), Caliph 'Abd al-Malik b. Marwan implemented the coinage reformation to promote Arabisation of coins, and in A. H. 87 (706), 'Abd Allahi b. 'Abd al-Malik, the governor- general of Egypt, pursued Arabisation of official documentation under a decree by Caliph Walid b. 'Abd al-Malik.(2) As a result, the Arabic letters came into the immediate use for the coin inscriptions and gradually for the official documents. However, when the figures were involved, the Greek or the Coptic numerals were used together with the Arabic letters.(3) The Abjad Arabic numerals were also created by assigning the numerical values to the Arabic alphabetic (abjad) letters just like the Greek numerals, but they did not spread very much.(4) It was in the latter half of the 8th century that the Indian numerals, generally regarded as the forerunners of the Arabic numerals, were introduced to the Islamic world. -
Arithmetical Proofs in Arabic Algebra Jeffery A
This article is published in: Ezzaim Laabid, ed., Actes du 12è Colloque Maghrébin sur l'Histoire des Mathématiques Arabes: Marrakech, 26-27-28 mai 2016. Marrakech: École Normale Supérieure 2018, pp 215-238. Arithmetical proofs in Arabic algebra Jeffery A. Oaks1 1. Introduction Much attention has been paid by historians of Arabic mathematics to the proofs by geometry of the rules for solving quadratic equations. The earliest Arabic books on algebra give geometric proofs, and many later algebraists introduced innovations and variations on them. The most cited authors in this story are al-Khwārizmī, Ibn Turk, Abū Kāmil, Thābit ibn Qurra, al-Karajī, al- Samawʾal, al-Khayyām, and Sharaf al-Dīn al-Ṭūsī.2 What we lack in the literature are discussions, or even an acknowledgement, of the shift in some authors beginning in the eleventh century to give these rules some kind of foundation in arithmetic. Al-Karajī is the earliest known algebraist to move away from geometric proof, and later we see arithmetical arguments justifying the rules for solving equations in Ibn al-Yāsamīn, Ibn al-Bannāʾ, Ibn al-Hāʾim, and al-Fārisī. In this article I review the arithmetical proofs of these five authors. There were certainly other algebraists who took a numerical approach to proving the rules of algebra, and hopefully this article will motivate others to add to the discussion. To remind readers, the powers of the unknown in Arabic algebra were given individual names. The first degree unknown, akin to our �, was called a shayʾ (thing) or jidhr (root), the second degree unknown (like our �") was called a māl (sum of money),3 and the third degree unknown (like our �#) was named a kaʿb (cube). -
Arabic Numeral
CHAPTER 4 Number Representation and Calculation Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 1 4.4 Looking Back at Early Numeration Systems Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 2 Objectives 1. Understand and use the Egyptian system. 2. Understand and use the Roman system. 3. Understand and use the traditional Chinese system. 4. Understand and use the Ionic Greek system. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 3 The Egyptian Numeration System The Egyptians used the oldest numeration system called hieroglyphic notation. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 4 Example: Using the Egyptian Numeration System Write the following numeral as a Hindu-Arabic numeral: Solution: Using the table, find the value of each of the Egyptian numerals. Then add them. 1,000,000 + 10,000 + 10,000 + 10 + 10 + 10 + 1 + 1 + 1 + 1 = 1,020,034 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 5 Example: Using the Egyptian Numeration System Write 1752 as an Egyptian numeral. Solution: First break down the Hindu-Arabic numeral into quantities that match the Egyptian numerals: 1752 = 1000 + 700 + 50 + 2 = 1000 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 10 + 10 + 10 + 10 + 10 + 1 + 1 Now use the table to find the Egyptian symbol that matches each quantity. Thus, 1752 can be expressed as Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 6 The Roman Numeration System Roman I V X L C D M Numeral Hindu- 1 5 10 50 100 500 1000 Arabic Numeral The Roman numerals were used until the eighteenth century and are still commonly used today for outlining, on clocks, and in numbering some pages in books. -
Toward a Poiesis of Curriculum Donna Lynn Trueit Louisiana State University and Agricultural and Mechanical College
Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2005 Complexifying the poetic: toward a poiesis of curriculum Donna Lynn Trueit Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Education Commons Recommended Citation Trueit, Donna Lynn, "Complexifying the poetic: toward a poiesis of curriculum" (2005). LSU Doctoral Dissertations. 2988. https://digitalcommons.lsu.edu/gradschool_dissertations/2988 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. COMPLEXIFYING THE POETIC: TOWARD A POIESIS OF CURRICULUM A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Curriculum and Instruction by Donna Lynn Trueit B. S. N., University of Victoria, 1994 M. A., University of Victoria, 1996 December 2005 © Copyright 2005 Donna Lynn Trueit All rights reserved ii DEDICATION To Bill (Dr. William E. Doll, Jr.), without whom this inquiry would have been impossible: your optimism, imagination, faith, intellect and love inspire and sustain me. iii ACKNOWLEDGMENTS This project was made possible by the incredible, intellectual atmosphere of inquiry in Curriculum and Instruction at LSU, in the Curriculum Theory Project, developed and promoted by Drs. William Pinar and William E. Doll, Jr. In this academically rich, challenging, stimulating, and welcoming environment, I took up the invitation, graciously extended, to partake. -
Origin of the Numerals Al-Biruni's Testimony
Origin of the numerals Al-Biruni’s testimony Ahmed Boucenna Laboratoire DAC, Department of Physics, Faculty of Sciences, Ferhat Abbas University 19000 Stif, Algeria [email protected] [email protected] Abstract The origin of the numerals that we inherited from the arabo-Islamic civilization remained one enigma. The hypothesis of the Indian origin remained, with controversies, without serious rival. It was the dominant hypothesis since more of one century. Its partisans found to it and constructed a lot of arguments. The testimonies of the medieval authors have been interpreted to its advantage. The opposite opinions have been dismissed and ignored. An amalgam between the history of our modern numerals and the Indian mathematics history is made. Rational contradictions often passed under silence. A meticulous observation of the numerals permits to affirm that our numerals are in fact more or less modified Arabic letters. The "Ghubari" shape of the numerals shows that the symbol of a numeral corresponds to the Arabic letter whose numerical value is equal to this numeral. The numerals don't have a simple resemblance with some Arabic letters, but every number looks like the Arabic letter whose numerical value is equal to this numeral. The elements of the ''Abjadi'' calculation gives us a theoretical support, independent of the letters and numerals, witch explains our observation. Besides a re-lecture of the testimonies of the medieval authors, particularly the testimony of Al-Biruni, that is probably at the origin of all others testimonies speaking of the Indian origin of the numerals, is in agreement with the fact that our numerals are Arabic letters. -
Islamic Mathematics
Islamic Mathematics Elizabeth Rogers MATH 390: Islamic Mathematics Supervised by Professor George Francis University of Illinois at Urbana-Champaign August 2008 1 0.1 Abstract This project will provide a summary of the transmission of Greek mathe- matics through the Islamic world, the resulting development of algebra by Muhammad ibn Musa al-Khwarizmi, and the applications of Islamic algebra in modern mathematics through the formulation of the Fundamental Theo- rem of Algebra. In addition to this, I will attempt to address several cultural issues surrounding the development of algebra by Persian mathematicians and the transmission of Greek mathematics through Islamic mathematicians. These cultural issues include the following questions: Why was the geometry of Euclid transmitted verbatim while algebra was created and innovated by Muslim mathematicians? Why didn't the Persian mathematicians expand or invent new theorems or proofs, though they preserved the definition-theorem-proof model for ge- ometry? In addition, why did the definition-theorem-proof model not carry over from Greek mathematics (such as geometry) to algebra? Why were most of the leading mathematicians, in this time period, Mus- lim? In addition, why were there no Jewish mathematicians until recently? Why were there no Orthodox or Arab Christian mathematicians? 0.2 Arabic Names and Transliteration Arabic names are probably unfamiliar to many readers, so a note on how to read Arabic names may be helpful. A child of a Muslim family usually receives a first name ('ism), followed by the phrase \son of ··· "(ibn ··· ). For example, Th¯abitibn Qurra is Th¯abit,son of Qurra. Genealogies can be combined; for example, Ibr¯ah¯ımibn Sin¯anibn Th¯abitibn Qurra means that Ibr¯ah¯ımis the son of Sin¯an,grandson of Th¯abit,and great-grandson of Qurra. -
The Islamic Connection
THE ISLAMIC CONNECTION CONTRIBUTIONS MADE BY THE ARABS TO MATHEMATICS by John E. Sasser, Ph.D. COPYRIGHT Copyright © 2007 by John E. Sasser. All rights reserved. No part of this paper may be reproduced in any form, electronic or mechanical, including photocopy recording, or any information storage or retrieval system, without permission in writing from the author. 2 The Arab Contribution to Mathematics CONTENTS Foreword...............................................……............... 4 Dedication..................................................…….......... 5 Preface........................................................…….......... 7 Map............................................................…….......... 9 List of Illustrations…………………………………... 10 Introduction..................................................……........ 11 The Search for Knowledge.....................…................. 23 Antiquity and the European Renaissance: Translations. Geometry: Geometric Constructions……………….. Trigonometry Direction Time NumberTheory: ……………………………………. The Hindu-Arabic Numeration System. Astronomy and the Calendar: Algebra: Conclusion..........................................……................. References........................................……................... Glossary……………………………………………... Index......................................................…….............. 3 The Arab Contribution to Mathematics FOREWORD This paper describes selected principal contributions to mathematics and the Arabs. Selection of appropriate examples to illustrate -
The Arabic-Latin Translators – Natural Science and Philosophy
CHARLES BURNETT List of Publications Books, and articles over 100 pages long Articles and pamphlets, arranged thematically, and in chronological order within each topic The Arabic-Latin Translators – Natural Science and Philosophy – Astronomy and Astrology - Medicine and Psychology – Magic and Divination – Arithmetic and Geometry – Anglo- Norman Science and Learning in the Twelfth Century – Peter Abelard and the French Schools – Music – Contacts between the West and the Far East – Miscellaneous – Reviews (selection) List of editions of Latin texts in books and articles above (Please note that some diacritical markings are missing) Books, and articles over 100 pages long: 1. Hermann of Carinthia, De essentiis, critical edition, translation and commentary, Leiden, 1982, 385 pp. (reviews in Speculum, 1984, pp. 911–3, Cahiers de civilisation médiévale, 28, 1985, p. 685, Mittellateinisches Jahrbuch, 20, 1985, pp. 287–90, Deutsches Archiv, 41, 1985, p. 255, Rivista di storia della filosofia, 2, 1984, pp. 349–51, Bulletin de théologie ancienne et médiévale, 14, 1989, p. 695). 2. ‘A Checklist of the Manuscripts Containing Writings of Peter Abelard and Heloise and Other Works Closely Associated with Abelard and his School’, Revue d’histoire des textes, 14–15, 1984–5, pp. 183–302 (with David Luscombe and Julia Barrow). 3. Pseudo-Bede, De mundi celestis terrestrisque constitutione: a Treatise on the Universe and the Soul, edition, translation and commentary, Warburg Institute Surveys and Texts 10, London, 1985. 88 pp. (reviews in Isis, 77, 1986, pp. 182–3, Revue d’histoire ecclésiastique, 81, 1986, p. 742, Ambix, 33, 1986, p. 155, Journal of the History of Astronomy, 19, 1988, pp. -
Amos Bertolacci
Amos Bertolacci ALBERTUS MAGNUS AND ‘AVENZORETH’ (IBN ZUR‘A, D. 1008 ): LEGEND OR REALITY? «Ricorda Baudolino… Il Presbyter Johannes… La via dell’Oriente…» «Basta che sia vero, e noi lo mettiamo», aveva detto Baudolino, «l’importante è non raccontare favole» (U. Eco, Baudolino ) Some of Albertus Magnus’ commentaries on Aristotle contain ref - erences to an unidentified author. Albertus calls him «Avenzoreth», according to what seems the most likely spelling of his name given by the manuscripts, and credits him with a very pessimistic view on the beastly nature of man and the lack of freedom in human condi - tion. The identity of this author has remained uncertain so fa r 1. In Albertus’ report, Avenzoreth shows legendary traits: he is presented as a priest, who lived in the East, and pronounced a severe admoni - tion against mankind. Despite this seemingly mythical profile, I wish to show that Avenzoreth corresponds to an Arabic author who really existed: there are good reasons to identify him with a theologian and philosopher active in Baghdad at the turn between the tenth and the eleventh century, Ab u¯ ‘Al ¯ı ‘Is a¯ Ibn Zur‘a. The quotations of Avenzoreth in Albertus Magnus are interesting for three main reasons. 1) This author is otherwise unknown in Latin philosophy: to the best of my knowledge, he is quoted by name only by Albertus Magnus. If, as I think, Avenzoreth is not the fruit of 1. Relevant information can be found in T. Ricklin, «Von den beatiores philosophi zum optimus status hominis . Zur Entradikalisierung der radikalen Aris - toteliker», in Geistesleben im 13 . -
The Contributions of Arab Civilization to Mathematics and Science
CLASSROOM The Contributions of Arab Civilization to Mathematicsand Science By JULIE PETEET sciences, literature, and diplomacy, and the Islamic Introduction cities became centers for the cultivation and teaching of the sciences and arts. From the second half of the eighth to the end of the With the Islamic / Arab conquests in the 7th century eleventh century, Arabic was the scientific, the pro A.D., a process of cultural assimilation began. Those gressive language of mankind .. .. When the West was sufficiently mature to feel the need of deeper people who came under Arab rule adopted the Arabic knowledge, it turned its attention, first of all, not to the language, Islam, and much of the culture of the Arabs, Greek sources, but to the Arabic ones. while the Arabs in turn adopted many of the cultural -George Sarton. Introdu ction 10 the History of traditions, skills, and knowledge of the various peoples Science, 1950. with whom they interacted. When we speak of " Arab science," we mean that (7'uring the Arab age of enlightenment, from the 7th Arabic was the language of science and scholarship, and O'--'to the 13th centuries A.D., the arts and sciences it was under the encouragement and patronage of the flourished under the patronage and encouragement of Arab Caliphs that science, art, and literature thrived the Islamic Empire. The intellectual endeavors and and prospered. The Islamic Empire brought together achievements of this period have had a lasting impact on peoples of various ethnic, linguistic, and religiou s the course of scientific thought throughout the rest of groups, but they shared a commonality in that Arabic the world.