Hubertus L.L. Busard (1923–2007)

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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 critical 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 information 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 centuries: 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. (ISBN: 3-515-07410-4) (Boethius, Band 41). 14. Johannes de Tinemue’s Redaction of Euclid’s Elements, the so-called Adelard III Version. Vol. I, II. Stuttgart, Franz Steiner Verlag, 2001, 632 pp. (ISBN: 3-515-07975-0) (Boethius, Band 45). 15. Campanus of Novara and Euclid’s Elements. Vol. I, II. Stuttgart, Franz Steiner Verlag, 2005, 768 pp. (ISBN: 3-515-08645-5) (Boethius, Band 51). 16. Nicole Oresme, Questiones super geometriam Euclidem. Stuttgart, Franz Steiner Verlag (to be published in the series “Boethius”).

Menso Folkerts Lehrstuhl für Geschichte der Naturwissenschaften, Museumsinsel 1, 80538 Munich, Germany E-mail address: [email protected]

Available online 8 October 2009