DOCSLIB.ORG

Hubertus L.L. Busard (1923–2007)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Hubertus L.L. Busard (1923–2007) View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Available online at www.sciencedirect.com Historia Mathematica 36 (2009) 317–320 www.elsevier.com/locate/yhmat In Memoriam Hubertus L.L. Busard (1923–2007) Hubertus Lambertus Ludovicus Busard was born on 21 August 1923 in Sittard (The Netherlands, Province of Limburg). After attending the classical (in Sittard) and scientific (in Heerlen) gymnasium he studied mathematics and physics at the University of Utrecht (1945–1949). From 1949 to 1951 he taught at gymnasia in Maastricht and in Heerlen. From 1951 to 1985, when he retired, he was lecturer in mathematics and later vice-director (“adjunct-directeur”) at the Polytechnic (Hogere Technische School) in Venlo. Already as a young man Busard was interested in the history of mathematics and related matters. Through his contact with his former classmate Joseph J. Kockelmans (1923–2008), who later became professor of philosophy at Pennsylvania State University, Busard Photograph published with the permission of Lé Giesen (Venlo, Netherlands). doi:10.1016/j.hm.2009.07.008 318 In Memoriam / Historia Mathematica 36 (2009) 317–320 widened his knowledge in the philosophy and theology of the Middle Ages. He decided to write a doctoral dissertation on medieval mathematics—an edition with commentary of the Questiones on Euclid’s Elements by Nicole Oresme (ca. 1320–1382). His supervisor was E.J. Dijksterhuis (1892–1965), though Busard mostly worked on his own. His doctorate was approved on 13 March 1961 at the University of Utrecht. Busard’s dissertation attracted the attention of the German historian of mathematics Joseph Ehrenfried Hofmann (1900–1973). He did his best to provide Busard with a position in the history of science at a university, but unfortunately failed. From 1963 to 1967 Busard was scientific assistant to Professor Jan Hendrik van den Berg (b. 1914) at the Institute for Psychology of Conflicts at the University of Leiden. Here Busard’s task was to investigate mathematical thought in the Latin West and the Arabic East and to compare the develop- ments in these cultures. Van den Berg insisted that Busard learn Arabic, and in conse- quence he studied Arabic in Leiden from 1964 to 1966 with G.W.J. Drewes (1899–1992). Because Busard and Van den Berg had essentially different research interests, the cooper- ation came to an early end. Hofmann had encouraged Busard, immediately after he finished his dissertation, to investigate the French mathematicians of the 16th and 17th centuries, in particular François Viète (1540–1603) and Claude Mydorge (1585–1647). In this connection Busard wrote several articles for the Dictionary of Scientific Biography. But since he had much more interest in the Middle Ages, he spent his free time editing medieval mathematical texts. When he started this work in 1961, many important mathematical texts were not yet available in critical editions. Marshall Clagett and his school on the one hand and Busard on the other are largely responsible for filling this gap. The main focus of Busard’s work consists of a series of editions of the medieval transla- tions and redactions of Euclid’s Elements, the most important textbook of Greek mathematics. This work was translated three times from the Arabic into Latin in the 12th century, by Adelard of Bath, Hermann of Carinthia and Gerard of Cremona; there were, furthermore, a translation directly from the Greek and two widespread reworkings from the 12th and 13th centuries by Robert of Chester and Campanus. Busard made crit- ical editions of eight versions, and, besides this, of further redactions, commentaries, etc. Some of the Euclid versions exist in dozens of manuscript copies, and from all of these the original readings had to be painstakingly reconstructed. Thanks to this incredible amount of work by a single scholar, now every important Latin version of the Elements is available. All historians of mathematics appreciate Marshall Clagett’s fundamental Archimedes in the Middle Ages (in five volumes, 1964–1984), which gives detailed informa- tion about the transmission and reception of Archimedes’ writings in Western Europe; Busard completed a similar task for “Euclid in the Middle Ages.” His editions are indis- pensable for every scholar interested in Euclid and his influence in the Middle Ages. Busard edited numerous other texts of the 12th to 15th centuries from the whole spectrum of mathematics. Particularly important are two extensive writings from the 13th and 14th cen- turies: De elementis arithmetice artis by Jordanus de Nemore, probably the most important medieval treatise on number theory, and De arte mensurandi by Johannes de Muris, a com- pendium of geometry. In the following we list the mathematical subjects of the further texts (with the names of the authors between parentheses) of which Busard presented editions1: 1 The bibliography found below only lists the books edited by Busard. A complete list of publications can be found in the obituary to be published in the Archives Internationales d’Histoire des Sciences. In Memoriam / Historia Mathematica 36 (2009) 317–320 319 various texts translated from the Arabic, in particular three on mensuration and one by Ahmad ibn Yusuf on spherical geometry; the treatise on isoperimetry that was translated directly from the Greek; theoretical arithmetic (by Johannes de Muris, Thomas Bradwardine, Wigandus Durnheimer); theory of proportions (by Jordanus de Nemore, Campanus, Albert of Saxony); infinite series; latitude of forms (Nicole Oresme); algorismus tracts, i.e. treatises on calculation with Hindu–Arabic numerals (by some authors in Jordanus de Nemore’s circle, by Johannes de Lineriis, and by one of the latter’s sources); practical geometry (by Dominicus de Clavasio); trigonometry (by Johannes of Gmunden). Through his work on critical editions Busard became perhaps the best-informed special- ist in medieval Western mathematics. Together with the author of this obituary, he pre- pared a bio-bibliographical handbook which will give information about all authors of medieval mathematical works in Latin and in the vernaculars, from Roman antiquity to the end of the 15th century. It is to be hoped that this work will be published in the next few years. Busard’s achievements were acknowledged by his election to corresponding (1971) and effective (1978) membership of the Académie Internationale d’Histoire des Sciences. On his 70th birthday he was honored by a Festschrift (Vestigia mathematica. Studies in medieval and early modern mathematics in honour of H.L.L. Busard, edited by M. Folkerts and J.P. Hogendijk; Amsterdam/Atlanta, Rodopi, 1993). Huub Busard died unexpectedly on 2 December 2007. He was a very loyal, friendly and helpful person. He lived modestly and placed little value on public honors. His work was only possible because all through the years he was unselfishly supported by his wife Yvonne, née Bollen, whom he married in 1951. He and his wife complemented each other and were happily married in a union based on Christian values. They had two children and five grandchildren. Huub Busard was an important historian of mathematics and an impressive person. He will not be forgotten. Books and monographs 1. Nicole Oresme, Quaestiones super geometriam Euclidis. Leiden, E.J. Brill, 1961, XIV + 179 pp. (Janus, Suppléments, vol. III). 2. Het rekenen met breuken in den middeleeuwen, in het bijzonder bij Johannes de Lineriis. Brussels, 1968, 36 pp. (Mededelingen van de Koninklijke Vlaamse Academie voor Wetenschappen, Letteren en Schone Kunsten van België. Klasse der Wetenschappen, Jaargang 30, nr. 7). 3. Quelques sujets de l’histoire des mathématiques au moyen-âge. Paris, 1969, 32 pp. (Conférences du Palais de la Découverte, D 125). 4. Der Tractatus proportionum von Albert von Sachsen. Vienna, 1971. (Österreichische Akademie der Wissenschaften. Mathematisch-naturwissenschaftliche Klasse, Denkschriften. 116. Band, 2. Abhandlung, pp. 43–72). 5. Der Traktat De sinibus, chordis et arcubus von Johannes von Gmunden. Vienna, 1971. (Öster- reichische Akademie der Wissenschaften. Mathematisch-naturwissenschaftliche Klasse, Denk- schriften. 116. Band, 3. Abhandlung pp. 73–113). 6. The Translation of the Elements of Euclid from the Arabic into Latin by Hermann of Carinthia (?). Books VII–XII. Amsterdam, Mathematisch Centrum, 1977, 198 pp. (ISBN: 90-6196-148- 3) (Mathematical Centre Tracts, 84). 320 In Memoriam / Historia Mathematica 36 (2009) 317–320 7. The Latin translation of the Arabic version of Euclid’s Elements commonly ascribed to Gerard of Cremona. Introduction, edition and critical apparatus. Leiden, New Rhine Publishers, 1983, XXVIII + 503 pp. (ISBN: 90-6227-993-7) (Asfar, Deel 2). 8. The First Latin Translation of Euclid’s Elements Commonly Ascribed to Adelard of Bath. Books I–VIII and Books X.36–XV.2. Toronto, Pontifical Institute of Mediaeval Studies, 1983, VI + 425 pp. (ISBN: 0-88844-064-2) (Studies and Texts, 64). 9. The Mediaeval Latin Translation of Euclid’s Elements Made Directly from the Greek. Stuttgart, Franz Steiner Verlag, 1987, 411 pp. (ISBN: 3-515-04628-3) (Boethius, Band 15). 10. Jordanus de Nemore, De elementis arithmetice artis. A Medieval Treatise on Number Theory. Part I: Text and Paraphrase. Part II: Conspectus Siglorum and Critical Apparatus. Stuttgart, Franz Steiner Verlag, 1991, 372 + 188 pp. (ISBN: 3-515-05214-3) (Boethius, Band 22). 11. (with Folkerts, Menso:) Robert of Chester’s (?) Redaction of Euclid’s Elements, the so-called Adelard II Version. Volume I, II. Basel/Boston/Berlin, Birkhäuser Verlag, 1992, 959 pp. (ISBN: 3-7643-2728-6) (Science Networks, vols. 8, 9). 12. A Thirteenth-Century Adaptation of Robert of Chester’s Version of Euclid’s Elements. 2 vols. München, Institut für Geschichte der Naturwissenschaften, 1996. 559 pp. (ISBN: 3-89241- 018-6) (Algorismus, Heft 17). 13. Johannes de Muris, De arte mensurandi. A Geometrical Handbook of the Fourteenth Century. Stuttgart, Franz Steiner Verlag, 1998, 392 pp.
Load more

Recommended publications
  • The Fifteenth-Seventeenth Century Transformation of Abbacus Algebra
    The fifteenth-seventeenth century transformation of abbacus algebra Perhaps – though not thought of by Edgar Zilsel and Joseph Needham – the best illustration of the ‘Zilsel-Needham thesis’ Summer School on the History of Algebra Institute for the History of the Natural Sciences Chinese Academy of Science 1–2 September 2011 Jens Høyrup Roskilde University Section for Philosophy and Science Studies http://www.akira.ruc.dk/~jensh PREPRINT 17 September 2011 Erik Stinus in memoriam Abstract In 1942, Edgar Zilsel proposed that the sixteenth–seventeenth-century emergence of Modern science was produced neither by the university tradition, nor by the Humanist current of Renaissance culture, nor by craftsmen or other practitioners, but through an interaction between all three groups in which all were indispensable for the outcome. He only included mathematics via its relation to the “quantitative spirit”. The present study tries to apply Zilsel’s perspective to the emergence of the Modern algebra of Viète and Descartes (etc.), by tracing the reception of algebra within the Latin-Universitarian tradition, the Italian abbacus tradition, and Humanism, and the exchanges between them, from the twelfth through the late sixteenth and early seventeenth century. Edgar Zilsel and the Zilsel-Thesis .............................. 1 The three acting groups ...................................... 3 Latin twelfth- to thirteenth-century reception ..................... 3 The fourteenth century – early abbacus algebra, and first interaction . 10 The fifteenth century
    [Show full text]
  • The History of Arabic Sciences: a Selected Bibliography
    THE HISTORY OF ARABIC SCIENCES: A SELECTED BIBLIOGRAPHY Mohamed ABATTOUY Fez University Max Planck Institut für Wissenschaftsgeschichte, Berlin A first version of this bibliography was presented to the Group Frühe Neuzeit (Max Planck Institute for History of Science, Berlin) in April 1996. I revised and expanded it during a stay of research in MPIWG during the summer 1996 and in Fez (november 1996). During the Workshop Experience and Knowledge Structures in Arabic and Latin Sciences, held in the Max Planck Institute for the History of Science in Berlin on December 16-17, 1996, a limited number of copies of the present Bibliography was already distributed. Finally, I express my gratitude to Paul Weinig (Berlin) for valuable advice and for proofreading. PREFACE The principal sources for the history of Arabic and Islamic sciences are of course original works written mainly in Arabic between the VIIIth and the XVIth centuries, for the most part. A great part of this scientific material is still in original manuscripts, but many texts had been edited since the XIXth century, and in many cases translated to European languages. In the case of sciences as astronomy and mechanics, instruments and mechanical devices still extant and preserved in museums throughout the world bring important informations. A total of several thousands of mathematical, astronomical, physical, alchemical, biologico-medical manuscripts survived. They are written mainly in Arabic, but some are in Persian and Turkish. The main libraries in which they are preserved are those in the Arabic World: Cairo, Damascus, Tunis, Algiers, Rabat ... as well as in private collections. Beside this material in the Arabic countries, the Deutsche Staatsbibliothek in Berlin, the Biblioteca del Escorial near Madrid, the British Museum and the Bodleian Library in England, the Bibliothèque Nationale in Paris, the Süleymaniye and Topkapi Libraries in Istanbul, the National Libraries in Iran, India, Pakistan..
    [Show full text]
  • Breaking the Circle: the Emergence of Archimedean Mechanics in the Late Renaissance
    Arch. Hist. Exact Sci. (2008) 62:301–346 DOI 10.1007/s00407-007-0012-8 Breaking the circle: the emergence of Archimedean mechanics in the late Renaissance Paolo Palmieri Received: 10 May 2007 / Published online: 10 August 2007 © Springer-Verlag 2007 Contents 1 Introduction: machines and equilibrium ................... 301 2 The a priori principles of scientia de ponderibus .............. 307 3 Center of gravity lost and found ....................... 314 4 An exploded drawing of mechanical reductionism ............. 321 5 Intermezzo: debunking the circle ...................... 325 6 The emergence of Archimedean mechanics ................. 329 7 Conclusion: surface phenomena, not deep roots ............... 336 Appendix. The workshop ............................. 337 1 Introduction: machines and equilibrium Imagine a weightless, rectilinear beam with two equal but punctiform weights fixed at its ends. The beam is free to rotate around its middle point, i.e., the fulcrum. I call this abstract machine a balance of equal arms (or balance, for brevity). If a balance is horizontal it will remain in equilibrium (as long as no external disturbances affect its state). What happens if a balance is inclined? Will it return to the horizontal position, or remain in equilibrium, like a horizontal balance? What happens if one weight is removed further from the fulcrum? Does a bent balance (i.e., a two-beam machine with Communicated by N. Swerdlow. P. Palmieri (B) Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260, USA e-mail: [email protected] 123 302 P. Palmieri two weightless arms rigidly joined on the fulcrum, one horizontal and one inclined, and with two equal punctiform weights fixed at their ends) behave like a balance of equal arms? Some late-medieval and Renaissance theorists of the so-called science of weights [scientia de ponderibus], such as Jordanus de Nemore (thirteenth century) and Niccolò Tartaglia (1500–1557), sought an a priori answer to these questions.
    [Show full text]
  • The Arabic Sources of Jordanus De Nemore
    The Arabic Sources of Jordanus de Nemore IMPORTANT NOTICE: Author: Prof. Menso Folkerts and Prof. Richard Lorch All rights, including copyright, in the content of this document are owned or controlled for these purposes by FSTC Limited. In Chief Editor: Prof. Mohamed El-Gomati accessing these web pages, you agree that you may only download the content for your own personal non-commercial Deputy Editor: Prof. Mohammed Abattouy use. You are not permitted to copy, broadcast, download, store (in any medium), transmit, show or play in public, adapt or Associate Editor: Dr. Salim Ayduz change in any way the content of this document for any other purpose whatsoever without the prior written permission of FSTC Release Date: July, 2007 Limited. Publication ID: 710 Material may not be copied, reproduced, republished, downloaded, posted, broadcast or transmitted in any way except for your own personal non-commercial home use. Any other use Copyright: © FSTC Limited, 2007 requires the prior written permission of FSTC Limited. You agree not to adapt, alter or create a derivative work from any of the material contained in this document or use it for any other purpose other than for your personal non-commercial use. FSTC Limited has taken all reasonable care to ensure that pages published in this document and on the MuslimHeritage.com Web Site were accurate at the time of publication or last modification. Web sites are by nature experimental or constantly changing. Hence information published may be for test purposes only, may be out of date, or may be the personal opinion of the author.
    [Show full text]
  • The Development of Mathematics in Medieval Europe by Menso Fol- Kerts Variorum Collected Studies Series CS811
    The Development of Mathematics in Medieval Europe by Menso Fol- kerts Variorum Collected Studies Series CS811. Aldershot, UK: Ashgate, 2006. Pp. xii + 340. ISBN 0--86078--957--8.Cloth. Reviewed by Jens Høyrup Roskilde, Denmark [email protected] This is Menso Folkerts’ second Variorum volume. The first was pub- lished in 2003 [see Høyrup 2007b for a review]; it contained papers dealing with the properly Latin tradition in European mathemat- ics, that is, the kind of mathematics which developed (mainly on the basis of agrimensor mathematics and the surviving fragments of Boethius’ translation of the Elements) before the 12th-century Arabo- Latin and Greco-Latin translations. This second volume deals with aspects of the development which took place after this decisive divide, from ca 1100 to ca 1500. Few scholars, if any, know more than Folkerts about medieval Latin mathematical manuscripts. It is, therefore, natural that the perspective on mathematics applied in the papers of this volume is on mathematics as a body of knowledge, in particular, as it is transmitted in and between manuscripts. To the extent that mathematics as an activity is an independent topic, it mostly remains peripheral, being dealt with through references to the existing literature—exceptions are the investigations of what Regiomontanus and Pacioli do with their Euclid [in articles VII and XI]—or it is undocumented, as when it is said that Jordanus de Nemore’s De numeris datis was ‘probably used as a university textbook for algebra’ [VIII.413]. There should be no need to argue, however, that familiarity with the body of mathe- matical knowledge is fundamental for the study of mathematics from any perspective: whoever is interested in medieval Latin mathemat- ics can therefore learn from this book.
    [Show full text]
  • A New Art in Ancient Clothes
    JENS H 0Y R U P Estratto da: A NEW ART IN ANCIENT CLOTHES PHYSIS ITINERARIES CHOSEN BETWEEN SCHOLASTICISM AND BAROQUE RIVISTA 1NTERNAZI0NALE IN ORDER TO MAKE ALGEBRA APPEAR LEGITIMATE, AND THEIR DI STORIA DELLA SCIENZA IMPACT ON THE SUBSTANCE OF THE DISCIPLINE V ol. XXXV (1998) N uova S erie Fa s c . 1 FIRENZE LEO S. OLSCHKI EDITORE MCMXCVIII A NEW ART IN ANCIENT CLOTHES ITINERARIES CHOSEN BETWEEN SCHOLASTICISM AND BAROQUE IN ORDER TO MAKE ALGEBRA APPEAR LEGITIMATE, AND THEIR IMPACT ON THE SUBSTANCE OF THE DISCIPLINE* Jens Hoyrup Roskilde University Copenaghen Dedicato a Gino Arrighi, in occasione dell’esordio del suo decimo decennio SUMMARY — A number of authors writing on algebra between 1200 and 1680 tried to conceal the non-classic origin of the discipline, or were convinced that its true origin had to be found with Greek mathematicians: thus for instance Jordanus of Nemore, Regiomontanus, Petrus Ramus, Bombelli, Viete, and Caramuel. They followed different strategies, demonstrating thus to understand the character of Greek mathematics in different ways. On their part, these different understandings influenced the ways the authors approached algebra. The impact of the attempt to connect algebra to ancient mathematics can be further highlighted by looking at authors who did not try to connect algebra to Greek mathematics - for instance Leonardo Fibonacci, Jean de Murs, and Cardano. * A preliminary version of the paper was presented at the seminar Histoire de la lecture des anciens en matkematiques, CIRM, Luminy-Marseille, 16-20 octobre 1995. I use the opportunity to thank the organizers for the invitation, and the participants for stimulating discussions.
    [Show full text]
  • Tartaglia's Science of Weights and Mechanics in the Sixteenth Century
    Raffaele Pisano • Danilo Capecchi Tartaglia's Science of Weights and Mechanics in the Sixteenth Century Selections from Quesiti et inventioni diverse: Books VII-VIII ^ Springer Contents Part I Biographical Sketches & Science in Context 1 Niccolo Tartaglia and the Renaissance Society Between Science and Technique 3 1.1 Niccolo Fontana Called Tartaglia 3 1.1.1 Biographical and Scientific Sketches 4 1.1.1.1 The Roots 12 1.1.1.2 Tartaglia's Education 14 1.1.1.3 Arnaldo Masotti, Tartaglia's Modern Editor. ... 17 1.1.2 Tartaglia's Conceptual Stream in the Renaissance 19 1.1.2.1 Mathematics: The Third Degree Equations 20 1.1.2.2 On the Geometry: Euclid's Elements 31 1.1.2.3 On the Arithmetics: Tartaglia's Triangle 35 1.1.2.4 On Physics: Ballistics 39 1.1.3 Physics and Architecture: On Ballistics & Fortifications . 49 1.1.3.1 On Ballistics & Technical Instruments in the Nova Scienta 49 1.1.3.2 The Sesto Libro on Fortifications 71 1.1.3.3 The Gionta del Sesto Libro 75 1.1.3.4 The Gionta del Sesto Libro and Architecture .... 80 1.1.4 On the Opera Archimedis and Archimedis de insidentibus aquae 87 1.1.4.1 On the Opera Archimedis (1543) 87 1.1.4.2 On the Archimedis de insidentibus aquae (1543; 1565) 92 XV xvi Contents 1.1.5 Contents, Former Pupils and Philological Notes 95 1.1.5.1 A Content of Quesiti' et inventiom' diverse 98 1.1.5.2 Scholars, Former Pupils, Correspondence and Commentaries in Quesiti and Around Tartaglia's Science 99 1.1.5.3 Philological Notes and a Historical Hypothesis 102 2 Ancient and Modern Statics in the Renaissance 113 2.1
    [Show full text]
  • The Enigma of the Inclined Plane from Hero to Galileo Sophie Roux, Egidio Festa
    The Enigma of the Inclined Plane from Hero to Galileo Sophie Roux, Egidio Festa To cite this version: Sophie Roux, Egidio Festa. The Enigma of the Inclined Plane from Hero to Galileo. Mechanics and Natural Philosophy before the Scientific Revolution, Kluwer Academic Publishers, pp.195-221, 2008. halshs-00806464 HAL Id: halshs-00806464 https://halshs.archives-ouvertes.fr/halshs-00806464 Submitted on 2 Apr 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THE ENIGMA OF THE INCLINED PLANE FROM HERON TO GALILEO 1 Sophie Roux and Egidio Festa The law of the inclined plane states that the ratio between a weight and the force needed to balance this weight on a given inclined plane is equal to the ratio between the length and the height of this plane. With the peremptory tone for which he is known, Descartes affirmed that this law was 2 known to “all those who write about mechanics”. Yet the problem of the inclined plane appears neither in Aristotle nor in Archimedes, and while writers such as Heron of Alexandria, Pappus of Alexandria, Leonardo da Vinci, Girolamo Cardano, and Colantonio Stigliola do indeed formulate it, they do not find the solution.
    [Show full text]
  • Roskilde University
    Roskilde University Jordanus de Nemore a case study on 13th century mathematical innovation and failure in cultural context Høyrup, Jens Published in: Philosophica Publication date: 1988 Document Version Early version, also known as pre-print Citation for published version (APA): Høyrup, J. (1988). Jordanus de Nemore: a case study on 13th century mathematical innovation and failure in cultural context. Philosophica, 42, s. 42. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain. • You may freely distribute the URL identifying the publication in the public portal. Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 28. Sep. 2021 JORDANUS DE NEMORE: A CASE STUDY ON 13TH CENTURY MATHEMATICAL INNOVATION AND FAILURE IN CULTURAL CONTEXT* [MANUSCRIPT] Jens Høyrup PRELIMINARY REFLECTIONS ON PRINCIPLES As a philosophically minded historian of science, I am mainly interested in the thought-style of whole periods; in the changes of such styles over time; and in the reasons which can be given for their existence and development and for the differences between the scientific thought-styles of different cultures.
    [Show full text]
  • An Archimedean Proposition Presented by the Brothers Banū Mūsā and Recovered in the Kitāb Al-Istikmāl (Eleventh Century)
    An Archimedean Proposition Presented by the Brothers Banū Mūsā and Recovered in the Kitāb al-Istikmāl (eleventh century) Lluís Pascual Abstract: Archimedes developed a geometrical method to obtain an approximation to the value of π , that appears in the encyclopaedic work of the prince al-Mu’taman ibn Hūd in the eleventh century. This article gives the edition, translation and transcription of this Archimedean proposition in his work, together with some comments about how other medieval authors dealt with the same proposition. Keywords: al-Mu’taman, Archimedes, al-Istikmāl , Banū Mūsā, Gerard of Cremona, al-Ṭūsī, the value of π, geometrical. Appearance of the proposition in Saragossa during the eleventh century There was a great burst of scientific activity in Saragossa during the eleventh century, especially in the fields of mathematics and philosophy. In mathematics, the most notable work produced in eleventh-century Saragossa was the « Kitāb al-Istikmāl », or « The book of perfection ». This encyclopaedic work was written by the prince al-Mu’taman ibn Hūd, who reigned from 1081 until the date of his death in 1085. His reign was very short, but during the very long reign of his father (al-Muqtadir ibn Hūd, king from 1046 to 1081) crown prince al-Mu’taman devoted himself to the study of mathematics, on subjects originated by Euclid and by others, and started the composition of the « Kitāb al-Istikmāl ». As Hogendijk has noted (Hogendijk, 1991) and (Hogendijk, 1995), al- Mu’taman sometimes transcribes the propositions as if he had copied them from Suhayl 14 (2015), pp. 115-143 116 Lluis Pascual their Euclidian origin, but more often he takes the initiative himself: he simplifies demonstrations, he merges symmetrical propositions into a single one, and he often changes the flow of the demonstration.
    [Show full text]
  • The Slow Development Toward Algebraic Symbolization in Abbacus- and Related Manuscripts, C
    MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2009 PREPRINT 390 Jens Høyrup Hesitating progress – the slow development toward algebraic symbolization in abbacus- and related manuscripts, c. 1300 to c.1550 Hesitating progress – the slow development toward algebraic symbolization in abbacus- and related manuscripts, c. 1300 to c. 1550 Jens Høyrup [email protected] http://www.akira.ruc.dk/~jensh Contribution to the conference Philosophical Aspects of Symbolic Reasoning in Early Modern Science and Mathematics Ghent, 27–29 August 2009 Before Italy ..................................................... 1 Latin algebra: Liber mahamaleth, Liber abbaci, translations of al-Khwa¯rizmı¯, and Jordanus .................................................... 7 Abbacus writings before algebra ...................................... 13 The beginning of abbacus algebra ..................................... 15 The decades around 1400 ........................................... 21 The mid-fifteenth-century abbacus encyclopediae ........................... 26 Late fifteenth-century Italy .......................................... 35 Summary observations about the German and French adoption ................. 40 Why should they? ................................................ 42 References ..................................................... 43 Manuscripts consulted ............................................. 49 Kurt Vogel nochmals in Erinnerung et en mémoire de Jean Cassinet Abstract From the early fourteenth century
    [Show full text]
  • Early History of Algebra: a Sketch January 19, 2004
    Math 113, Spring 2004 Professor Mariusz Wodzicki Early History of Algebra: a Sketch January 19, 2004 Algebra has its roots in the theory of quadratic equations which obtained its original and quite full development in ancient Akkad (Mesopotamia) at least 3800 years ago. In Antiquity, this earliest Algebra greatly influenced Greeks1 and, later, Hindus. Its name, however, is of Arabic origin. It attests to the popularity in Europe of High Middle Ages of Liber algebre et almuchabole — the Latin translation of the short treatise on the subject of solving quadratic equations: H . AJº Ë@ Al-kitabu¯ ’l-muhtasaru f¯ı hisabi¯ ’l-gabriˇ wa-’l-muqabalati¯ (A é ÊK.A®Ü Ï@ð Q .m.Ì'@H. Ak ú¯ Qå JjÜ Ï@ – . summary of the calculus of gebr and muqabala). The original was composed circa AD 830 in Arabic at the House of Wisdom—a kind of academy in Baghdad where in IX-th century a number of books were compiled or translated into Arabic chiefly from Greek and Syriac sources—by some Al-Khwarizmi2 whose name simply means that he was a native of the ancient city of Khorezm (modern Uzbekistan). Three Latin translations of his work are known: by Robert of Chester (executed in Segovia in 1140), by Gherardo da Cremona3 (Toledo, ca. 1170) and by Guglielmo de Lunis (ca. 1250). Al-Khwarizmi’s name lives today in the word algorithm as a monument to the popularity of his other work, on Indian Arithmetic, which circulated in Europe in several Latin versions dating from before 1143, and spawned a number of so called algorismus treatises in XIII-th and XIV-th Centuries.
    [Show full text]