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Sur une construction du miroir parabolique par Abū al-Wafā´ al-Būzjānī

Published online by Cambridge University Press:  24 October 2008

Otto Neugebauer
Affiliation:
Institute for Advanced Study, Princeton
Roshdi Rashed
Affiliation:
Centre d'histoire des sciences et des philosophies arabes et médiévales, 7 rue Guy Môquet, B.P. n˚ 8, 94801 Villejuif Cedex, France

Abstract

Abū al-Wafā’ al-Būzjānī proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Būzjānī's contemporaries, like al-Qūhī and Ibn Sahl, i.e. on the methods of conical projections. The second method borrowed by al-Būzjānī from Ibn Sinān seems to support this last interpretation.

Abū al-Wafā’ al-Būzjānī a proposé, dans un fragment établi et traduit ici, deux méthodes pour construire le miroir parabolique. L'absence de démonstration, notamment pour la première méthode, soulève la difficile question de l'interprétation. Pour comprendre cette méthode, O. Neugebauer a eu recours, dans un article – non publié – traduit ici, à des notions de géométrie descriptive. II a ensuite éliminé la construction spatiale utilisée, pour ne garder que des considérations géométriques simples, connues des Grecs. La seconde interprétation, donnée par R. Rashed, s'inspire des pratiques géométriques des contemporains d'al-Būzjānī, comme al-Qūhī et Ibn Sahl, c'est-à-dire des méthodes des projections coniques. La seconde méthode empruntée par al-Būzjānī à Ibn Sinān semble corroborer cette dernière interprétation.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1999

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References

1 Rashed, R., Œuvres philosophiques et scientifiques d'al-Kindī, Vol. I: L'optique et la catoptrique (Leiden, 1997).Google Scholar

2 Rashed, R., “A pioneer in anaclastics. Ibn Sahl on burning mirrors and lenses,” Isis, 81 (1990): 464–91CrossRefGoogle Scholar et Géométrie et dioptrique au Xe siècle: Ibn Sahl, al-Qūhī et Ibn al-Haytham (Paris, 1993).Google Scholar

3 Les catoptriciens grecs. I: Les miroirs ardents. Édition, traduction et commentaire par Rashed, R., Collection des Universités de France, Paris, sous presse.Google Scholar

4 Rashed, Voir R., “Al-Qūhī vs. Aristotle: On motion”, Arabic Sciences and Philosophy, 9.1 (1999): 724, et Gémétrie et dioptrique au Xe siècle.CrossRefGoogle Scholar

5 Cf. Woepcke, F., “Recherches sur l'historie des sciences mathématiques chez les Orientaux, d'après des traités inédits arabes et persans”, Journal asiatique, série 5, tome 5 (1855): 309–59, à la p. 326.Google Scholar

6 Voir, The Works of Ibrahim ibn Sinan, ed. Saidan, A. S. (Kuwait, 1983), pp. 41–4.Google Scholar

* Ce texte a été établi à partir des manuscrits suivants:

[A] Istanbul, Süleymaniye, Aya Sofya 2753, fols. 14–16.

[D] Le Caire, Dār al-Kutub, Riyāḍa 260, fols. 10v–12r.

[Q] Le Caire, Dār al-Kutub, Riyāḍa 366, fols. 7r-8r.

Une ancienne version persane de ce texte a été établie et traduite par Chavoshi, J. Aghayani, L'œuvre scientifique d'Abū al-Wafā' al-Būzjānī, Thèse soutenue à l'Université Paris 7 (1997) non publiée.Google Scholar

7 Le quart de son diamètre.

8 Au quart de la droite AB.

3
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